8th Grade 3D Geometry 2015-11-20 www.njctl.org Slide 3 / 97 - - PDF document

Slide 1 / 97

8th Grade

3D Geometry

2015-11-20 www.njctl.org

Slide 2 / 97 Table of Contents

· Prisms and Cylinders

Volume

· Pyramids, Cones & Spheres Click on the topic to go to that section

More Practice/ Review 3-Dimensional Solids Glossary & Standards

Slide 3 / 97

Table of Contents

· Prisms and Cylinders

Volume

· Pyramids, Cones & Spheres Click on the topic to go to that section

More Practice/ Review 3-Dimensional Solids Glossary & Standards

[This object is a pull tab]

Teacher Notes

Vocabulary Words are bolded in the presentation. The text box the word is in is then linked to the page at the end

• f the presentation with the

word defined on it.

Slide 3 (Answer) / 97

3-Dimensional Solids

Return to Table of Contents

Slide 4 / 97

The following link will take you to a site with interactive 3-D figures and nets.

Slide 5 / 97

Polyhedron A 3-D figure whose faces are all polygons. Polyhedron Not Polyhedron Sort the figures into the appropriate side.

Polyhedron Slide 6 / 97 3-Dimensional Solids

Categories & Characteristics of 3-D Solids: Prisms

• 1. Have 2 congruent, polygon bases which are parallel

to one another

• 2. Sides are rectangular (parallelograms)
• 3. Named by the shape of their base

Pyramids

• 1. Have 1 polygon base with a vertex opposite it
• 2. Sides are triangular
• 3. Named by the shape of their base

click to reveal click to reveal

Slide 7 / 97 3-Dimensional Solids

Categories & Characteristics of 3-D Solids: Cylinders

• 1. Have 2 congruent, circular bases which

are parallel to one another

• 2. Sides are curved

Cones

• 1. Have 1 circular bases with a vertex opposite it
• 2. Sides are curved

click to reveal click to reveal

Slide 8 / 97

Edge Line segment formed where 2 faces meet Vertex (Vertices) Point where 3 or more faces/edges meet

3-Dimensional Solids

Vocabulary Words for 3-D Solids: Polyhedron A 3-D figure whose faces are all polygons (Prisms & Pyramids) Face Flat surface of a Polyhedron

Slide 9 / 97

Sort the figures. If you are incorrect, the figure will be sent back.

Slide 10 / 97

1 Name the figure. A Rectangular Prism B Triangular Pyramid C Hexagonal Prism D Rectangular Pyramid E Cylinder F Cone

Slide 11 / 97

1 Name the figure. A Rectangular Prism B Triangular Pyramid C Hexagonal Prism D Rectangular Pyramid E Cylinder F Cone

[This object is a pull tab]

Answer

D

Slide 11 (Answer) / 97

2 Name the figure. A Rectangular Pyramid B Triangular Prism C Octagonal Prism D Circular Pyramid E Cylinder F Cone

Slide 12 / 97

2 Name the figure. A Rectangular Pyramid B Triangular Prism C Octagonal Prism D Circular Pyramid E Cylinder F Cone

[This object is a pull tab]

Answer

E

Slide 12 (Answer) / 97

3 Name the figure. A Rectangular Pyramid B Triangular Pyramid C Triangular Prism D Hexagonal Pyramid E Cylinder F Cone

Slide 13 / 97

3 Name the figure. A Rectangular Pyramid B Triangular Pyramid C Triangular Prism D Hexagonal Pyramid E Cylinder F Cone

[This object is a pull tab]

Answer

B

Slide 13 (Answer) / 97

4 Name the figure. A Rectangular Prism B Triangular Prism C Square Prism D Rectangular Pyramid E Cylinder F Cone

Slide 14 / 97

4 Name the figure. A Rectangular Prism B Triangular Prism C Square Prism D Rectangular Pyramid E Cylinder F Cone

[This object is a pull tab]

Answer

A

Slide 14 (Answer) / 97

5 Name the figure. A Rectangular Prism B Triangular Pyramid C Circular Prism D Circular Pyramid E Cylinder F Cone

Slide 15 / 97

5 Name the figure. A Rectangular Prism B Triangular Pyramid C Circular Prism D Circular Pyramid E Cylinder F Cone

[This object is a pull tab]

Answer

F

Slide 15 (Answer) / 97

For each figure, find the number of faces, vertices and edges. Can you figure out a relationship between the number of faces, vertices and edges of 3-Dimensional Figures?

Name Faces Vertices Edges Cube 6 8 12 Rectangular Prism 6 8 12 Triangular Prism 5 6 9 Triangular Pyramid 4 4 6 Square Pyramid 5 5 8 Pentagonal Pyramid 6 6 10 Octagonal Prism 10 16 24

Math Practice

Slide 16 / 97 Euler's Formula

F + V = E + 2 Euler's Formula is the number of edges plus 2 is equal to the sum of the faces and vertices.

Slide 17 / 97

6 How many faces does a pentagonal prism have?

Slide 18 / 97

6 How many faces does a pentagonal prism have?

[This object is a pull tab]

Answer

7

Slide 18 (Answer) / 97

7 How many edges does a rectangular pyramid have?

Slide 19 / 97

7 How many edges does a rectangular pyramid have?

[This object is a pull tab]

Answer

8

Slide 19 (Answer) / 97

8 How many vertices does a triangular prism have?

Slide 20 / 97

8 How many vertices does a triangular prism have?

[This object is a pull tab]

Answer

6

Slide 20 (Answer) / 97

9 How many faces does a hexagonal pyramid have?

Slide 21 / 97

9 How many faces does a hexagonal pyramid have?

[This object is a pull tab]

Answer

7

Slide 21 (Answer) / 97

10 How many vertices does a triangular pyramid have?

Slide 22 / 97

10 How many vertices does a triangular pyramid have?

[This object is a pull tab]

Answer

4

Slide 22 (Answer) / 97

Volume

Return to Table of Contents

Slide 23 / 97

Label

• Units3 or cubic units

Volume

Volume

• The amount of space occupied by a 3-D Figure
• The number of cubic units needed to FILL a 3-D Figure (layering)

click to reveal click to reveal

Slide 24 / 97

Label

• Units3 or cubic units

Volume

Volume

• The amount of space occupied by a 3-D Figure
• The number of cubic units needed to FILL a 3-D Figure (layering)

click to reveal click to reveal [This object is a pull tab]

Math Practice

MP.6: Attend to Precision. Ask: What labels (or units) should we use with our answers?

Slide 24 (Answer) / 97

Volume Activity

Click the link below for the activity. Lab #1: Volume Activity

Slide 25 / 97 Volume Activity

Click the link below for the activity. Lab #1: Volume Activity

[This object is a pull tab]

Teacher Notes

The URL for the lab is: http://njctl.org/courses/ math/8th-grade-math/3d- geometry/volume-activity/

Slide 25 (Answer) / 97

Volume of Prisms & Cylinders

Return to Table of Contents

Slide 26 / 97

Volume

Volume of Prisms & Cylinders: Area of Base x Height, or V = Bh Area Formulas: Rectangle = lw or bh Triangle = bh or 2 Circle = πr2

click to reveal

(bh) 1 2

click to reveal click to reveal click to reveal

Slide 27 / 97 Find the Volume

5 m 8 m 2 m

Slide 28 / 97 Find the Volume

5 m 8 m 2 m

[This object is a pull tab]

Answer

VOLUME: 2 x 5 10 (Area of Base) x 8 (Height) 80 m3 VOLUME: V = B h V = l w h V = 5 2 8 V = 10 8 V = 80 m3

Slide 28 (Answer) / 97

Find the Volume

Use 3.14 as your value of π.

10 yd 9 yd

Slide 29 / 97 Find the Volume

Use 3.14 as your value of π.

10 yd 9 yd

[This object is a pull tab]

Answer VOLUME: 9 x 9 81 x 3.14 254.34 x 10 2543.4 yd3

VOLUME: V = B h V = r2 h V = 3.14 92 10 V = 3.14 81 10 V = 254.34 10 V = 2543.4 yd3

(Area of Base) (Height)

Slide 29 (Answer) / 97

A cylinder with a radius measuring 2 cm and a height of 5 cm is compared to a cylinder with a radius of 4 cm and a height of 5 cm. Amy says that the volume of the cylinder with a radius of 4 cm is double the volume of the cylinder with a radius of 2 cm. She used 3.14 as her value of π. Is she correct? Explain your reasoning. Start by calculating the volume of both cylinders. V = (3.14)(2)2(5) V = 62.8 cm3 V = (3.14)(4)2(5) V = 251.2 cm3 Answer the question. No, Amy is not correct. If the radius of the cylinder doubles, the volume does not double. Instead it quadruples.

click click click

Find the Volume Slide 30 / 97

A cylinder with a radius measuring 2 cm and a height of 5 cm is compared to a cylinder with a radius of 4 cm and a height of 5 cm. Amy says that the volume of the cylinder with a radius of 4 cm is double the volume of the cylinder with a radius of 2 cm. She used 3.14 as her value of π. Is she correct? Explain your reasoning. Start by calculating the volume of both cylinders. V = (3.14)(2)2(5) V = 62.8 cm3 V = (3.14)(4)2(5) V = 251.2 cm3 Answer the question. No, Amy is not correct. If the radius of the cylinder doubles, the volume does not double. Instead it quadruples.

click click click

Find the Volume

[This object is a pull tab]

Math Practice

MP.3 - Construct viable arguments & critique the reasoning of others.

After calculating the volume of both cylinders, ask: What do you think about what Amy predicted? Do you agree? Why or Why not?

Slide 30 (Answer) / 97

Teachers: Use this Mathematical Practice Pull Tab for the next 9 SMART Response slides.

Slide 31 / 97

Teachers: Use this Mathematical Practice Pull Tab for the next 9 SMART Response slides.

[This object is a pull tab]

Math Practice

MP.5 - Use appropriate tools strategically.

Ask: Can you make a model to show that? Would it help to create a diagram/draw a picture?

Slide 31 (Answer) / 97

4 in 11 Find the Volume. 7 in

1 5

1 in

1 2

Slide 32 / 97

4 in 11 Find the Volume. 7 in

1 5

1 in

1 2

[This object is a pull tab]

Answer VOLUME: 7.2 x 1.5 10.8 (Area of Base) x 4 (Height) 43.2 in

3

VOLUME: V = B h V = 7.2(1.5)(4) V = 43.2 in

3

Slide 32 (Answer) / 97

12 Find the volume of a rectangular prism with length 2 cm, width 3.3 cm and height 5.1 cm.

Slide 33 / 97

12 Find the volume of a rectangular prism with length 2 cm, width 3.3 cm and height 5.1 cm.

[This object is a pull tab]

Answer

VOLUME: V = B h V =2(3.3)(5.1) V = (6.6)(5.1) V = 33.66 cm

3

Slide 33 (Answer) / 97

13 Which is a possible length, width and height for a rectangular prism whose volume = 18 cm 3 A 1 x 2 x 18 B 6 x 3 x 3 C 2 x 3 x 3 D 3 x 3 x 3

Slide 34 / 97

13 Which is a possible length, width and height for a rectangular prism whose volume = 18 cm 3 A 1 x 2 x 18 B 6 x 3 x 3 C 2 x 3 x 3 D 3 x 3 x 3

[This object is a pull tab]

Answer

C

Slide 34 (Answer) / 97

14 Find the volume. 21 ft 42 ft 50 ft 47 ft

Slide 35 / 97

14 Find the volume. 21 ft 42 ft 50 ft 47 ft

[This object is a pull tab]

Answer

V = Bh & B = bh of the triangle V = (21)(42)(50) V = (882)(50) V = 441(50) V = 22,050 ft3 1 2 1 2 1 2

Slide 35 (Answer) / 97

15 A box-shaped refrigerator measures 12 by 10 by 7 on the outside. All six sides of the refrigerator are 1 unit

• thick. What is the inside volume of the refrigerator in

cubic units? HINT: You may want to draw a picture!

Slide 36 / 97

15 A box-shaped refrigerator measures 12 by 10 by 7 on the outside. All six sides of the refrigerator are 1 unit

• thick. What is the inside volume of the refrigerator in

cubic units? HINT: You may want to draw a picture!

[This object is a pull tab]

Answer

10 in. 7 in. 12 in. 8 in. 5 i n . 10 in.

Slide 36 (Answer) / 97

16 Find the volume. Use 3.14 as your value of π.

6 m 10 m

Slide 37 / 97

16 Find the volume. Use 3.14 as your value of π.

6 m 10 m

[This object is a pull tab]

Answer

d = 10 m, so r = 5 m V = r2 h V = 3.14 52 6 V = 3.14 25 6 V = 78.5 6 V = 471 m3

Slide 37 (Answer) / 97

17 Which circular glass holds more water? Note: Use 3.14 as your value of π. A Glass A having a 7.5 cm diameter and standing 12 cm high B Glass B having a 4 cm radius and a height

• f 11.5 cm

Slide 38 / 97

17 Which circular glass holds more water? Note: Use 3.14 as your value of π. A Glass A having a 7.5 cm diameter and standing 12 cm high B Glass B having a 4 cm radius and a height

• f 11.5 cm

[This object is a pull tab]

Answer Glass A d = 7.5, so r = 3.75 V = B h V = r2 h V = 3.14 (3.75)2 12 V = 3.14 14.0625 12 V = 529.875 cm3 Glass B V = B h V = r2 h V = 3.14 (4)2 11.5 V = 3.14 16 11.5 V = 577.76 cm3

Slide 38 (Answer) / 97

18 What is the volume of the largest cylinder that can be placed into a cube that measures 10 feet on an edge? Use 3.14 as your value of π.

Slide 39 / 97

18 What is the volume of the largest cylinder that can be placed into a cube that measures 10 feet on an edge? Use 3.14 as your value of π.

[This object is a pull tab]

Answer

d = 10 ft, so r = 5 ft & h = 10 ft V = π (52)(10) V = π (25)(10) V = 785 ft3

Slide 39 (Answer) / 97

19 A circular garden has a diameter of 20 feet and is surrounded by a concrete border that has a width

• f three feet and a depth of 6 inches. What is the

volume of concrete in the path? Use 3.14 as your value of π.

Slide 40 / 97

19 A circular garden has a diameter of 20 feet and is surrounded by a concrete border that has a width

• f three feet and a depth of 6 inches. What is the

volume of concrete in the path? Use 3.14 as your value of π.

[This object is a pull tab]

Answer

dinner = 20, so rinner = 10 ft router = 10 + 3 = 13 ft V = Bh = πr2h V = [π(132) - π(102)] (0.5) V = (169π - 100π)(0.5) V = (216.66)(0.5) V = 108.33 ft3

Slide 40 (Answer) / 97

Sometimes, a question will ask you to "Leave your answer in terms of π". This means that you treat π like a variable & only do the arithmetic operations with the remaining numbers. Ex: If a cylinder has a radius of 3 and a height of 4, then Volume = π(3)2(4) = π(9)(4) = 36π units2 Let's try some more problems like this one.

Click here to return to cones & spheres.

Answer in Terms of π Slide 41 / 97

Leave your answer in terms of π.

10 yd 9 yd

Find the Volume Slide 42 / 97

Leave your answer in terms of π.

10 yd 9 yd

Find the Volume

[This object is a pull tab]

Answer

VOLUME: V = B h V = r2 h V = 92 10 V = 81 10 V = 810 yd3

Slide 42 (Answer) / 97

30 ft 15 ft

Leave your answer in terms of π.

Find the Volume Slide 43 / 97

30 ft 15 ft

Leave your answer in terms of π.

Find the Volume

[This object is a pull tab]

Answer

d = 15, so r = 7.5 VOLUME: V = B h V = r2 h V = (7.5)2 30 V = 56.25 30 V = 1687.5 ft3

Slide 43 (Answer) / 97

20 A cylinder has a radius of 7 and a height of 2. What is its volume? Leave your answer in terms of π. A 14π units3 B 28π units3 C 49π units3 D 98π units3

Slide 44 / 97

20 A cylinder has a radius of 7 and a height of 2. What is its volume? Leave your answer in terms of π. A 14π units3 B 28π units3 C 49π units3 D 98π units3

[This object is a pull tab]

Answer

V = Bh V = (7)2 2 V = 49 2 V = 98 units3

π π π

D

Slide 44 (Answer) / 97

21 A cylinder has a diameter of 12 in. and a height of 12 in. What is its volume? Leave your answer in terms of π. A 144π in3 B 432π in3 C 864π in3 D 1,728π in3

Slide 45 / 97

21 A cylinder has a diameter of 12 in. and a height of 12 in. What is its volume? Leave your answer in terms of π. A 144π in3 B 432π in3 C 864π in3 D 1,728π in3

[This object is a pull tab]

Answer

d = 12 in., so r = 6 in. V = Bh V = (6)2 12 V = 36 12 V = 432 in3

π π π

B

Slide 45 (Answer) / 97

22 A cylinder has a diameter of 17 in. and a height of 5 in. What is its volume? Leave your answer in terms of π. A 106.25π in3 B 361.25π in3 C 425π in3 D 1,228.25π in3

Slide 46 / 97

22 A cylinder has a diameter of 17 in. and a height of 5 in. What is its volume? Leave your answer in terms of π. A 106.25π in3 B 361.25π in3 C 425π in3 D 1,228.25π in3

[This object is a pull tab]

Answer

d = 17 in., so r = 8.5 in. V = Bh V = (8.5)2 5 V = 72.25 5 V = 361.25 in3

π π π

B

Slide 46 (Answer) / 97

23 A circular pool has a diameter of 40 feet and is surrounded by a wooden deck that has a width of 4 feet and a depth of 6 inches. What is the volume of the wooden deck? Leave your answer in terms of π. A 88π ft3 B 176π ft3 C 400π ft3 D 576π ft3

Slide 47 / 97

23 A circular pool has a diameter of 40 feet and is surrounded by a wooden deck that has a width of 4 feet and a depth of 6 inches. What is the volume of the wooden deck? Leave your answer in terms of π. A 88π ft3 B 176π ft3 C 400π ft3 D 576π ft3

[This object is a pull tab]

Answer

pool: d = 40 ft, so r = 20 ft deck: r = 20 + 4 = 24 ft V = ( (24)2 - (20)2)(0.5) V = (576 - 400 )0.5 V = 176 (0.5) V = 88 ft3

π π π π π π

A

Slide 47 (Answer) / 97

Volume of Pyramids, Cones & Spheres

Return to Table of Contents

Slide 48 / 97 Slide 49 / 97

Slide 49 (Answer) / 97 Demonstration comparing volume of Cones & Spheres with volume of Cylinders

click to go to web site

Slide 50 / 97

(Area of Base x Height) = Bh

1

3

1

3 A cone is 1/3 the volume of a cylinder with the same base area (B) and height (h). Area of Base x Height 3 Bh 3 =

Volume of a Cone

click to reveal

Slide 51 / 97

V = 2/3 (Volume of Cylinder) r2 h ( ) 2/3 V=

• r

V = 4/3 r3

π π Volume of a Sphere

A sphere is 2/3 the volume of a cylinder with the same base area (B) and height (h).

click to reveal

Slide 52 / 97

V = 2/3 (Volume of Cylinder) r2 h ( ) 2/3 V=

• r

V = 4/3 r3

π π Volume of a Sphere

A sphere is 2/3 the volume of a cylinder with the same base area (B) and height (h).

click to reveal [This object is a pull tab]

Figure

Slide 52 (Answer) / 97

How much ice cream can a Friendly’s Waffle cone hold if it has a diameter of 6 in and its height is 10 in? Use 3.14 as your value of π. (Just Ice Cream within Cone. Not on Top) Volume and Mass used in portion control. $$$

Volume Slide 53 / 97

How much ice cream can a Friendly’s Waffle cone hold if it has a diameter of 6 in and its height is 10 in? Use 3.14 as your value of π. (Just Ice Cream within Cone. Not on Top) Volume and Mass used in portion control. $$$

Volume

[This object is a pull tab]

Answer & Math Practice

V = (3.14)(32)(10) V = 92.3 in3 1 3 Questions to address MP.1: What information are you given? What is this problem asking? Questions to address MP.4: Write a number sentence to model this problem. What connections do you see?

Slide 53 (Answer) / 97

24 Find the volume. Use 3.14 as your value of π.

4 in 9 in

Slide 54 / 97

24 Find the volume. Use 3.14 as your value of π.

4 in 9 in

[This object is a pull tab]

Answer

V = Bh V = (π 42)(9) V = (16π )(9) V = 3(50.24) V = 150.72 in3 1 3 1 3 1 3

Slide 54 (Answer) / 97

25 Find the Volume. Use 3.14 as your value of π. 5 cm 8 cm

Slide 55 / 97

25 Find the Volume. Use 3.14 as your value of π. 5 cm 8 cm

[This object is a pull tab]

Answer

V = Bh V = (π 52)(8) V = (25π )(8) V = (200π ) V = 209 cm3 1 3 1 3 1 3 1 3 1 3

Slide 55 (Answer) / 97

V = πr3 V = (3.14)(5.5)3 V = 696.6 cm3 4 3 4 3 If the radius of a sphere is 5.5 cm, what is its volume? Use 3.14 as your value of π.

Click here

Volume Slide 56 / 97

26 What is the volume of a sphere with a radius of 8 ft? Use 3.14 as your value of π.

Slide 57 / 97

26 What is the volume of a sphere with a radius of 8 ft? Use 3.14 as your value of π.

[This object is a pull tab]

Answer

V = π r3 V = (3.14)(8)3 V = 2,143.57 ft3 4 3 4 3

Slide 57 (Answer) / 97

27 What is the volume of a sphere with a diameter of 4.25 in? Use 3.14 as your value of π.

Slide 58 / 97

27 What is the volume of a sphere with a diameter of 4.25 in? Use 3.14 as your value of π.

[This object is a pull tab]

Answer

d = 4.25, so r = 2.125 V = π r3 V = (3.14)(2.125)3 V = 40.17 in3 4 3 4 3

Slide 58 (Answer) / 97

Similar to when we found the volume of a cylinder, with a cone and a sphere, you could be asked to "Leave your answer in terms of π". Click here if you need to review that property.

Volume in Terms of π Slide 59 / 97

You are selling lemonade in conic cups (cups shaped like cones). How much lemonade will each customer get to drink? Leave your answer in terms of π.

8 cm 11 cm

Volume in Terms of π Slide 60 / 97

You are selling lemonade in conic cups (cups shaped like cones). How much lemonade will each customer get to drink? Leave your answer in terms of π.

8 cm 11 cm

Volume in Terms of π

[This object is a pull tab]

Answer

d = 8 cm, so r = 4 cm V = (4)2 (11) V = (16)(11) V = cm3 = 58.6 cm3 1 3 1 3

π π π

176 3

π

Slide 60 (Answer) / 97

If the radius of a sphere is 6 cm, what is its volume? Leave your answer in terms of π.

Volume in Terms of π Slide 61 / 97

If the radius of a sphere is 6 cm, what is its volume? Leave your answer in terms of π.

Volume in Terms of π

[This object is a pull tab]

Answer

V = (6)3 V = (216) V = cm3 V = 288 cm3 4 3 4 3

π π π

864 3

π

Slide 61 (Answer) / 97

28 Find the volume of the cone below. Leave your answer in terms of π. A 12π in3 B 36π in3 C 48π in3 D 144π in3

4 in 9 in

Slide 62 / 97

28 Find the volume of the cone below. Leave your answer in terms of π. A 12π in3 B 36π in3 C 48π in3 D 144π in3

4 in 9 in

[This object is a pull tab]

Answer

V = (4)2 (9) V = (16)(9) V = (16)(3) V = 48 in3 1 3 1 3

π π π π

C

Slide 62 (Answer) / 97

29 Find the volume of the sphere that has a diameter of 18

• cm. Leave your answer in terms of π.

A 729π cm3 B 972π cm3 C 5,832π cm3 D 7,776π cm3

Slide 63 / 97

29 Find the volume of the sphere that has a diameter of 18

• cm. Leave your answer in terms of π.

A 729π cm3 B 972π cm3 C 5,832π cm3 D 7,776π cm3

[This object is a pull tab]

Answer

d = 18 cm, so r = 9 cm V = (9)3 V = (729) V = V = 972 cm3 4 3 4 3

π π π π

2916 3 B

Slide 63 (Answer) / 97

30 Find the volume of the cone below. Leave your answer in terms of π. A 49π in3 B 84π in3 C 147π in3 D 252π in3

7 in 12 in

Slide 64 / 97

30 Find the volume of the cone below. Leave your answer in terms of π. A 49π in3 B 84π in3 C 147π in3 D 252π in3

7 in 12 in

[This object is a pull tab]

Answer

d = 7 in., so r = 3.5 in. V = (3.5)2 (12) V = (12.25)(12) V = (12.25)(4) V = 49 in3 1 3 1 3

π π π π

A

Slide 64 (Answer) / 97

31 Find the volume of a sphere that has a radius of 4.5 cm. Leave your answer in terms of π. A 27π cm3 B 91.125π cm3 C 121.5π cm3 D 364.5π cm3

Slide 65 / 97

31 Find the volume of a sphere that has a radius of 4.5 cm. Leave your answer in terms of π. A 27π cm3 B 91.125π cm3 C 121.5π cm3 D 364.5π cm3

[This object is a pull tab]

Answer

V = (4.5)3 V = (91.125) V = V = 121.5 cm3 4 3 4 3

π π π π

364.5 3 C

Slide 65 (Answer) / 97

32 A sphere with a radius measuring 9 cm is compared to a sphere with a radius of 18 cm. Jeff says that the volume

• f the sphere with a radius of 18 cm is double the volume
• f the sphere with a radius of 9 cm. Is he correct?

Explain your reasoning. When you are done calculating your answer, type in the number "1".

Slide 66 / 97

32 A sphere with a radius measuring 9 cm is compared to a sphere with a radius of 18 cm. Jeff says that the volume

• f the sphere with a radius of 18 cm is double the volume
• f the sphere with a radius of 9 cm. Is he correct?

Explain your reasoning. When you are done calculating your answer, type in the number "1".

[This object is a pull tab]

Answer

V = (9)3 V = (729) V = V = 972 cm3 4 3 4 3

π π π π

2,916 3 V = (18)3 V = (5,832) V = V = 7,776 cm3 4 3 4 3

π π π π

23,328 3 7,776 is not double the volume

• f 972 . It's 8 times bigger.

π π

Slide 66 (Answer) / 97

(Area of Base x Height) = Bh

1

3

1

3 Area of Base x Height 3 Bh 3 =

Volume of a Pyramid

A pyramid is 1/3 the volume of a prism with the same base area (B) and height (h).

click to reveal

Slide 67 / 97

Pyramids are named by the shape of their base.. The volume is a pyramid is 1/3 the volume of a prism with the same base area(B) and height (h). V = Bh

1 3

=5 m side length = 4 m V = Bh V = (4)(4)(5) V = (80) V = 26 m3 1 3 1 3 1 3 2 3

Click here

Pyramids Slide 68 / 97

33 Find the Volume of a triangular pyramid with a base edge of 8 in, base height of 4 in and a pyramid height

• f 10 in.

8 in 10 in 4 in

Slide 69 / 97

33 Find the Volume of a triangular pyramid with a base edge of 8 in, base height of 4 in and a pyramid height

• f 10 in.

8 in 10 in 4 in

[This object is a pull tab]

Answer V = Bh V = [ (4)(8)](10) V = [ (32)](10) V = (16)(10) V = 53 in3 1 3 1 3 1 3 1 3 1 3 1 2 1 2

Slide 69 (Answer) / 97

34 Find the volume. 8 cm 7 cm 15.3 cm

Slide 70 / 97

34 Find the volume. 8 cm 7 cm 15.3 cm

[This object is a pull tab]

Answer V = Bh V = (8)(7)(15.3) V = (56)(15.3) V = 285.6 cm3 1 3 1 3 1 3

Slide 70 (Answer) / 97

More Practice / Review

Return to Table of Contents

Slide 71 / 97

35 Find the volume. 15 mm 8 mm 22 mm

Slide 72 / 97

35 Find the volume. 15 mm 8 mm 22 mm

[This object is a pull tab]

Answer

V = Bh V = (15)(8)(22) V = 880 mm3 1 3 1 3

Slide 72 (Answer) / 97

36 Find the volume of a rectangular pyramid with a base length of 2.7 meters and a base width of 1.3 meters, and the height of the pyramid is 2.4 meters. HINT: Drawing a diagram will help!

Slide 73 / 97

36 Find the volume of a rectangular pyramid with a base length of 2.7 meters and a base width of 1.3 meters, and the height of the pyramid is 2.4 meters. HINT: Drawing a diagram will help!

[This object is a pull tab]

Answer

V = Bh V = (2.7)(1.3)(2.4) V = 2.808 m3 1 3 1 3

Slide 73 (Answer) / 97

37 Find the volume of a square pyramid with base edge

• f 4 inches and pyramid height of 3 inches.

Slide 74 / 97

37 Find the volume of a square pyramid with base edge

• f 4 inches and pyramid height of 3 inches.

[This object is a pull tab]

Answer

V = Bh V = (42)(3) V = 16 in3 1 3 1 3

Slide 74 (Answer) / 97

38 Find the Volume. 9 m 9 m 12 m 11 m 6 m

Slide 75 / 97

38 Find the Volume. 9 m 9 m 12 m 11 m 6 m

[This object is a pull tab]

Answer

V = Bh V = [ (9)(6)](11) V = (27)(11) V = 99 m3 1 3 1 3 1 2 1 3

Slide 75 (Answer) / 97

39 Find the Volume. Use 3.14 as your value of π. 14 ft 21 ft

Slide 76 / 97

39 Find the Volume. Use 3.14 as your value of π. 14 ft 21 ft

[This object is a pull tab]

Answer

V = Bh V = π (72)(21) V = (3.14)(49)(21) V = 1,077.02 ft3 1 3 1 3 1 3

Slide 76 (Answer) / 97

40 Find the Volume. Use 3.14 as your value of π. 8 in 6.9 in

Slide 77 / 97

40 Find the Volume. Use 3.14 as your value of π. 8 in 6.9 in

[This object is a pull tab]

Answer

V = Bh V = π (42)(6.9) V = (3.14)(16)(6.9) V = 115.552 in3 1 3 1 3 1 3

Slide 77 (Answer) / 97

41 Find the Volume. 4 ft 7 ft 8 ft 9 ft

Slide 78 / 97

41 Find the Volume. 4 ft 7 ft 8 ft 9 ft

[This object is a pull tab]

Answer

V = Bh V = 7(4) (8) 2 V= 112 ft

3

Slide 78 (Answer) / 97

42 A cone 20 cm in diameter and 14 cm high was used to fill a cubical planter, 25 cm per edge, with

• soil. How many full cones of soil were needed to

fill the planter? 20 cm 14 cm 25 cm

Slide 79 / 97

42 A cone 20 cm in diameter and 14 cm high was used to fill a cubical planter, 25 cm per edge, with

• soil. How many full cones of soil were needed to

fill the planter? 20 cm 14 cm 25 cm

[This object is a pull tab]

Answer

Cone Cube 1/3(3.14)(102)(14) 253 1465.3 cm3 15625 cm3 15625/1465.3 # 10.7 about 11 cones

Slide 79 (Answer) / 97

43 Find the Volume. 7 in 8 in 9 in 9 in

2 in

Slide 80 / 97

43 Find the Volume. 7 in 8 in 9 in 9 in

2 in

[This object is a pull tab]

Answer

V = Bh V = 7(2) (8) 2 V= 56 in3

Slide 80 (Answer) / 97 Name a 3-D Figure that is not a polyhedron. Slide 81 / 97

Name a 3-D Figure that is not a polyhedron.

[This object is a pull tab]

Answer

possible answers cylinder cone

Slide 81 (Answer) / 97 Name a 3-D figure that has 6 rectangular faces. Slide 82 / 97 Name a 3-D figure that has 6 rectangular faces.

[This object is a pull tab]

Answer

rectangular prism

Slide 82 (Answer) / 97

44 Find the volume. 40 m 70 m 80 m

Slide 83 / 97

44 Find the volume. 40 m 70 m 80 m

[This object is a pull tab]

Answer

V = Bh V = 80(40)(70) V = 224,000 m3

Slide 83 (Answer) / 97

45 The figure shows a right circular cylinder and a right

circular cone. The cylinder and the cone have the same base and the same height. Part A: What is the volume of the cone, in cubic feet?

From PARCC EOY sample test calculator #11

A 12π ft3 B 16π ft3 C 36π ft3 D 48π ft3

Slide 84 / 97

45 The figure shows a right circular cylinder and a right

circular cone. The cylinder and the cone have the same base and the same height. Part A: What is the volume of the cone, in cubic feet?

From PARCC EOY sample test calculator #11

A 12π ft3 B 16π ft3 C 36π ft3 D 48π ft3

[This object is a pull tab]

Answer

V = (4)2 (3) V = (16)(3) V = (16) V = 16 ft3 1 3 1 3

π π π π

B Slide 84 (Answer) / 97

46 Part B: What is the ratio of the cone's volume to the cylinder's volume?

Slide 85 / 97

46 Part B: What is the ratio of the cone's volume to the cylinder's volume?

[This object is a pull tab]

Answer

Cylinder: V = (4)2(3) V = (16)(3) V = 48 ft3

π π π π

Cone: V = 16 ft3 Ratio = = 16π 48π 1 3

Slide 85 (Answer) / 97

Glossary & Standards

Return to Table of Contents

Slide 86 / 97

Glossary & Standards

Return to Table of Contents

[This object is a pull tab]

Teacher Notes

Vocabulary Words are bolded in the presentation. The text box the word is in is then linked to the page at the end

• f the presentation with the

word defined on it.

Slide 86 (Answer) / 97

tip traffic cone cone pencil ice cream

Back to Instruction

curved polyhedron surface

Cone

A polyhedron that has one circular base with a vertex opposite of it and sides that are curved. Slide 87 / 97

candles pizza Pringles can

Back to Instruction

curved polyhedron surface

Cylinder

A polyhedron that has two congruent circular bases which are parallel to one another and sides that are curved.

Slide 88 / 97

Back to Instruction

Edge

Line segment formed where 2 faces meet.

A triangular pyramid has 6 edges.

Slide 89 / 97

Back to Instruction

Euler's Formula

The number of edges plus 2 is equal to the sum of the faces and vertices. E + 2 = F + V E + 2= F + V E + 2 = 4 + 4 E + 2 = 8 E = 6 faces = 4 vertices = 4 pyramid: Slide 90 / 97

Back to Instruction

Face

Flat surface of a polyhedron.

A triangular pyramid has 4

• faces. (there is
• ne you can't see)

Slide 91 / 97

Back to Instruction

Polyhedron

A 3-D figure whose faces are all polygons. Cubes Prisms Pyramids

Made of: Faces Edges Vertices

Cylinders

Cones Slide 92 / 97

Rectangular

Prism

Triangular

Prism

Pris m

Pentagonal

Back to Instruction

Prism

A polyhedron that has two congruent, polygon bases which are parallel to one another, sides that are rectangular, and named by the shape of their base.

Block of cheese body

• f

pencil juice box

Slide 93 / 97

Pentagonal Pyramid Square Pyramid Triangular Pyramid

Back to Instruction

Pyramid

A polyhedron that has one polygon base with a vertex opposite of it,sides that are triangular, and named by the shape of its base. Slide 94 / 97

Back to Instruction

Vertex

Point where two or more straight lines/ faces/edges meet. A Corner.

A triangular pyramid has 4 vertices.

Slide 95 / 97

Back to Instruction

Volume

The number of cubic units needed to fill a 3D figure (layering). The amount of space occupied by a 3D figure.

Label:

Units3

• r

cubic units

volume

• f prisms

and cylinders: area of base x height

V = area of base x h V = 2m x 5m x 8m V = 80m3

Slide 96 / 97

Standards for Mathematical Practices

Click on each standard to bring you to an example of how to meet this standard within the unit.

MP8 Look for and express regularity in repeated reasoning. MP1 Make sense of problems and persevere in solving them. MP2 Reason abstractly and quantitatively. MP3 Construct viable arguments and critique the reasoning of others. MP4 Model with mathematics. MP5 Use appropriate tools strategically. MP6 Attend to precision. MP7 Look for and make use of structure.

Slide 97 / 97