1. Volume of Prisms and Cylinders Lesson 12.4

2. Volume of a solid is the number of cubic units of space contained by the solid.
The volume of a right rectangular prism is equal to the product of its length, its width, and its height.
V = lwh

3. Find the volume of the rectangular prism.
V = lwh
V = 14(7)(4)
V = 392 m3 4m 7m
14m

4. Find the height of the rectangular prism:
Theorem 115: The volume of a right rectangular prism is equal to the product of the height and the area of the base. V = Bh, where B is the area of the base.
Find the height of the rectangular prism:
V = Bh
3300 = 300h
11 = h
V = 3300
B = 300 h

5. Find the volume of any figure.
Theorem 116: The volume of any prism is equal to the product of the height and the area of the base.
V = Bh

6. Find the volume of the cylinder. V = Лr2h V = Л42(24) V = 384Л in3
Theorem 117: The volume of a cylinder is equal to the product of the height and the area of the base.
V = Bh
V = Лr2h
Find the volume of the cylinder.
V = Лr2h
V = Л42(24)
V = 384Л in3
24in
d = 8in

7. Cross-Section of a prism or cylinder.
A cross section is the intersection of a solid with a plane.
Theorem 118: The volume of a prism or a cylinder is equal to the product of the figure’s cross sectional area and its height.
V = Ch, where C is the area of the cross section.

8. Find the volume of the triangular prism.
V = Bh
Find the area of the base.
Base = ½ bh = ½ (12)(8) = 48
V = 48(15)
V = 720 units3

9. Find the volume. Break it into smaller parts. Vtop = 10(2)(5) = 100
Vbottom = 7(10)(4) = 280
Total Volume = = 380 units3