1. Volume
Unit 2

2. Warm Up
Josh marked off a section of the playground in the shape of a right triangle. If the hypotenuse of the triangular section measure 20 meters and one of the legs measures 6 meters, what is the area of the section of the playground?
If Josh needs to build a fence around his section, how much fencing would he need? Give the answer in meters.

3. Objectives:
Find the volume of a prism, pyramid, cone, cylinder, and sphere
Review other area and volume formulas

4. Vocabulary
A prism is a three-dimensional figure named for the shape of its bases. The two bases are congruent polygons. All of the other faces are parallelograms.
A cylinder has two circular bases.
A pyramid is named for the shape of its base. The base is a polygon, and all of the other faces are triangles.

5. More Vocabulary
A cone has a circular base. The height of a pyramid or cone is measured from the highest point to the base along a perpendicular line.
A sphere is the set of points in three dimensions that are a fixed distance from a given point, the center. A plane that intersects a sphere through its center divides the two halves or hemispheres. The edge of a hemisphere is a great circle.

6. If all six faces of a rectangular prism are squares, it is a cube.
Remember!
Triangular prism
Rectangular prism
Cylinder
Height
Height
Height
Base
Base
Base

7. Words Numbers Formula VOLUME OF PRISMS AND CYLINDERS
Prism: The volume V of a prism is the area of the base B times the height h.
Cylinder: The volume of a cylinder is the area of the base B times the height h.
B = 2(5)
= 10 units2
V = Bh
V = 10(3)
= 30 units3
B = p(22)
V = Bh
= 4p units2
= (pr2)h
V = (4p)(6) = 24p
 75.4 units3

8. VOLUME OF PYRAMIDS AND CONES
(22)

10. Volume Formula Summary
Pyramid:
Prism:
Cylinder: or
Cone: or
Sphere:

11. Try This: Example 1A
Find the volume of the figure to the nearest tenth.
A. A rectangular prism with base 5 mm by 9 mm and height 6 mm.
B = 5 • 9 = 45 mm2
Area of base
V = Bh
Volume of prism
= 45 • 6
= 270 mm3

12. Try This: Example 1B
Find the volume of the figure to the nearest tenth.
B = p(82)
Area of base B.
8 cm
= 64p cm2
V = Bh
Volume of a cylinder
15 cm
= (64p)(15) = 960p
 3,014.4 cm3

13. Try This: Example 1C
Find the volume of the figure to the nearest tenth. C.
B = • 12 • 10 1 2
Area of base
10 ft
= 60 ft2
V = Bh
Volume of a prism
14 ft
= 60(14)
= 840 ft3
12 ft

14. Additional Example 1B: Finding the Volume of Pyramids and Cones
Find the volume of the figure. B.
B = (32) = 9 in2 1 3
V = • 9 • 10
V = Bh 1 3
V = 30  94.2 in3
Use 3.14 for .

15. Try This: Example 1B
Find the volume of the figure. B.
B = (32) = 9 m2
7 m 1 3
V = • 9 • 7
V = Bh 1 3
3 m
V = 21  65.9 m3
Use 3.14 for .

16. Additional Example 1: Finding the Volume of a Sphere
Find the volume of a sphere with radius 9 cm, both in terms of p and to the nearest tenth of a unit. 4 3
V = pr3
Volume of a sphere
= p(9)3 4 3
Substitute 9 for r.
= 972p cm3  3,052.1 cm3

17. Lesson Quiz: Part 2
5. A basketball has a circumference of 29 in. To the nearest cubic inch, what is its volume?
412 in3

18. 1. the triangular pyramid 6.3 m3
Lesson Quiz: Part 1
Find the volume of each figure to the nearest tenth. Use 3.14 for p.
1. the triangular pyramid
6.3 m3
2. the cone
78.5 in3

19. Additional Example 2A: Exploring the Effects of Changing Dimensions
A juice box measures 3 in. by 2 in. by 4 in. Explain whether tripling the length, width, or height of the box would triple the amount of juice the box holds.
The original box has a volume of 24 in3. You could triple the volume to 72 in3 by tripling any one of the dimensions. So tripling the length, width, or height would triple the amount of juice the box holds.

20. Additional Example 2B: Exploring the Effects of Changing Dimensions
A juice can has a radius of 2 in. and a height of 5 in. Explain whether tripling the height of the can would have the same effect on the volume as tripling the radius.
By tripling the height, you would triple the volume. By tripling the radius, you would increase the volume to nine times the original.