Holt CA Course 1 10-8 Volume of Prisms Warm Up Warm Up Lesson Presentation Lesson Presentation...

Holt CA Course 1

10-8 Volume of Prisms

Warm UpWarm Up

Lesson PresentationLesson Presentation

California StandardsCalifornia Standards

PreviewPreview

Holt CA Course 1


Warm UpFind the area of each figure. Use 3.14 as an estimate for .

96 in2

50.24 ft2

1. rectangle with base length 8 in. and height 12 in.

2. circle with diameter 8 ft

Holt CA Course 1


MG1.3 Know and use the formulas for the volume of triangular prisms and cylinders (area of base × height); compare these formulas and explain the similarity between them and the formula for the volume of a rectangular solid.Also covered: AF3.1, AF3.2

California Standards

Holt CA Course 1


Vocabulary

volume

Holt CA Course 1


Volume is the number of cubic units needed to fill a space.

Holt CA Course 1


You need 10, or 5 · 2, centimeter cubes to cover the bottom of this rectangular prism.

You need 3 layers of 10 cubes each to fill the prism. It takes 30, or 5 · 2 · 3, cubes.

Holt CA Course 1


Volume is expressed in cubic units, so the volume of the prism is 5 cm · 2 cm · 3 cm = 30 cubic centimeters, or 30 cm3.

Holt CA Course 1


The volume of a rectangular prism is the area of its base times its height. This formula can be used to find the volume of any prism.

Holt CA Course 1

10-8 Volume of PrismsAdditional Example 1: Finding the Volume of a

Rectangular Prism

Find the volume of the rectangular prism.

B = 26 · 11 The base is a rectangle.

Multiply.B = 286

13 in.

26 in.11 in.

Step 1: Find the area of the base.

Holt CA Course 1

10-8 Volume of PrismsAdditional Example 1 Continued


V = Bh Write the formula.

V = 286 • 13 Substitute for B and h.

Multiply.V = 3,718 in3

13 in.

26 in.11 in.

Step 2: Find the volume.

The volume of the prism is 3,718 in3.

Holt CA Course 1

10-8 Volume of PrismsCheck It Out! Example 1


B = 29 · 12 The base is a rectangle.

Multiply.B = 348


16 in.

29 in.12 in.

Holt CA Course 1

10-8 Volume of PrismsCheck It Out! Example 1 Continued



V = 348 • 16 Substitute for B and h.

Multiply.V = 5,568 in3


The volume of the prism is 5,568 in3.

16 in.

29 in.12 in.

Holt CA Course 1


You can also use the formula V= Bh to find the volume of a triangular prism. For triangular prisms, B represents the area of a triangle, rather than a rectangle.

Holt CA Course 1


Triangular Prism

Find the volume of each triangular prism.

A. Step 1: Find the area of the base.

The base is a triangle.B = ( • 3.9 • 1.3) 12__

Multiply.B = 2.535

Holt CA Course 1


Triangular Prism


A. Step 2: Find the volume.


V = 2.535 • 4 Substitute for B and h.

Multiply.V = 10.14 m3

The volume of the prism is 10.14 m3.

Holt CA Course 1


The height of a prism is the distance between its two bases.

Caution!

Holt CA Course 1


Triangular Prism


B. Step 1: Find the area of the base.

The base is a triangle.B = ( • 6.5 • 7) 12__

Multiply.B = 22.75

Holt CA Course 1


Triangular Prism


B. Step 2: Find the volume.



Multiply.V = 136.5 ft3

The volume of the prism is 136.5 ft3.

Holt CA Course 1



A. Step 1: Find the area of the base.

The base is a triangle.B = ( • 4.2 • 1.6) 12__

Multiply.B = 3.36

1.6 m 7 m

4.2 m

Holt CA Course 1



A. Step 2: Find the volume.



Multiply.V = 23.52 m3

The volume of the prism is 23.52 m3.

1.6 m 7 m

4.2 m

Holt CA Course 1



B. Step 1: Find the area of the base.

The base is a triangle.B = ( • 4.5 • 9) 12__

Multiply.B = 20.25

4.5 ft5 ft

9 ft

Holt CA Course 1



B. Step 2: Find the volume.



Multiply.V = 101.25 ft3

The volume of the prism is 101.25 ft3.

4.5 ft5 ft

9 ft

Holt CA Course 1


Additional Example 3: Application

An artist wants to make glass paper-weights with the dimensions shown. He estimates that he will need less than 20 cubic centimeters of glass for each paperweight. Is his estimate reasonable? Explain.


The base is a triangle.B = • 6 • 5.2 = 15.612__

5.2 cm

6 cm

3 cm

Holt CA Course 1

10-8 Volume of PrismsAdditional Example 3 Continued

An artist wants to make glass paper-weights with the dimensions shown. He estimates that he will need less than 20 cubic centimeters of glass for each paperweight. Is his estimate reasonable? Explain.

Step 2: Find the volume.5.2 cm

6 cm

3 cm


V = 15.6 • 3 = 46.8 cm3 Substitute for B and h.

No; each paperweight will require about 47 cm3 of glass.

Holt CA Course 1


Check It Out! Example 3

An architect wants to make a model building with the dimensions shown. He estimates that he will need more than 60 cubic centimeters of paper for each building. Is his estimate reasonable? Explain.


The base is a triangle.B = • 6 • 5.5 = 16.512__

5.5 cm

6 cm

5 cm

Holt CA Course 1




V = 16.5 • 5 = 82.5 cm3 Substitute for B and h.

No; each building will require about 83 cm3 of paper.

5.5 cm

6 cm

5 cm

Check It Out! Example 3 Continued

An architect wants to make a model building with the dimensions shown. He estimates that he will need more than 60 cubic centimeters of paper for each building. Is his estimate reasonable? Explain.

Holt CA Course 1

10-8 Volume of PrismsLesson Quiz

Find the volume of each figure.

1. rectangular prism with length 20 cm, width

15 cm, and height 12 cm

2. triangular prism with a height of 12 cm and a

triangular base with base length 7.3 cm and

height 3.5 cm

3. Find the volume of the figure shown.

3,600 cm3

153.3 cm3

38.13 cm3

Holt CA Course 1 10-8 Volume of Prisms Warm Up Warm Up Lesson Presentation Lesson Presentation...

Documents

Transcript of Holt CA Course 1 10-8 Volume of Prisms Warm Up Warm Up Lesson Presentation Lesson Presentation...