Chapter 10 Lesson 5

1
Chapter 10 Lesson 5

• Objective To find the volume of a prism and a
  cylinder.

2
Theorem 10-6

• Volume of a Prism

h
Volume
Height
Base Area
Base Area

• Remember the Base Area formula will be
  determined by the base shape.

3
Volume of a Prism
height
width
length
Volume length x width x height
4
Example 1 Volume of a Prism

• What is the volume of a prism with dimensions 10
  cm, 8 cm and 5 cm.

5 cm
8 cm
10 cm
Volume length x width x height
Volume 10 x 8 x 5
Volume 400 cm3
5
Example 2 Volume of a Prism
What is the volume of the prism?
V l x w x h
V 4 x 2 x 10
V 80 cm3
10 cm
2 cm
4 cm
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Example 3 Volume of a Rectangular Prism
What is the volume of the prism?
V lwh
(13)(3)(5) 195 cm3
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Example 4 Volume of a Triangular Prism

• Find the volume of the triangular prism.

4cm 5cm
14cm
Volume ½ (length x width) x height
Volume ½ (5 x 4) x 14
Volume ½ (20) x 14
Volume 10 x 14
Volume 140cm3
8
Example 5 Volume of a Triangular Prism

• Find the volume of the triangular prism.

Volume ½ (length x width) x height
Volume ½ (3 x 4) x 12
12 cm
Volume ½ (12) x 12
Volume 6 x 12
3 cm
4 cm
5 cm
5 cm
h
3 cm
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Example 6 Volume of a Triangular Prism

• Find the volume of the triangular prism.

4.1cm
4.9cm
6.2cm
8.6cm
Volume ½ (length x width) x height
Volume ½ (8.6 x 4.1) x 6.2
Volume ½ (35.26) x 6.2
Volume 17.63 x 6.2
Volume 109.3 cm3
10
Theorem 10-7

• Volume of a Cylinder

Base Area
Radius
Volume
Height
Base Area
h
Base Area
Radius
11
Example 1 Volume of a Cylinder

• Find the volume of a cylinder with height 10 cm
  and radius 5 cm.

5 cm
10 cm
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Example 2 Volume of a Cylinder

• Find the volume of the cylinder.

9 ft
6 ft
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Example 3 Volume of a Cylinder
Find the volume of the cylinder. Give your
answers in terms of ? and rounded to the nearest
tenth.
V ?r2h
?(9)2(14)
1134? in3 ? 3562.6 in3
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Composite Figures
A composite space figure is a three-dimensional
figure that is the combination of two or more
simpler figures.
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Example 5 Composite Figures
Use a composite space figure to estimate the
volume of the backpack shown.     
Prism V lwh (12 4)11 528
Sum of the two volumes 528 226 754 The
approximate volume of the backpack is 754 in.3.
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Assignment
Page 547 1-19