1. volume of prisms and cylinders

2. What is volume?

3. A prism is a three-dimensional figure named for the shape of its bases
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.

4. 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

5. VOLUME OF PRISMS AND CYLINDERS
Words
Numbers
Formula
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

6. Area is measured in square units. Volume is measured in cubic units.
Helpful Hint

9. Additional Example 1A: Finding the Volume of Prisms and Cylinders
Find the volume of each figure to the nearest tenth.
A. A rectangular prism with base 2 cm by 5 cm and height 3 cm.
B = 2 • 5 = 10 cm2
Area of base
V = Bh
Volume of a prism
= 10 • 3
= 30 cm3

10. Additional Example 1B: Finding the Volume of Prisms and Cylinders
Find the volume of the figure to the nearest tenth. B.
B = p(42) = 16p in2
Area of base
4 in.
V = Bh
Volume of a cylinder
12 in.
= 16p • 12
= 192p  in3

11. Additional Example 1C: Finding the Volume of Prisms and Cylinders
Find the volume of the figure to the nearest tenth.
B = • 6 • 5 = 15 ft2 1 2 C.
Area of base
5 ft
V = Bh
Volume of a prism
= 15 • 7
= 105 ft3
7 ft
6 ft

12. 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

13. 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

14. 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

15. Lesson Quiz
Find the volume of each figure to the nearest tenth. Use 3.14 for p.
10 in. 1. 2. 3.
2 in.
12 in.
12 in.
10.7 in.
15 in.
3 in.
8.5 in.
942 in3
306 in3
160.5 in3