1. Volume 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 = l wh

3. Find the volume of the rectangular prism. 14m 4m 7m V = l wh V = 14(7)(4) V = 392 m 2

4. 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 = 3300 B = 300 h V = Bh 3300 = 300h 11 = 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. Theorem 117: The volume of a cylinder is equal to the product of the height and the area of the base. V = Bh V = Л r 2 h d = 8in 24in Find the volume of the cylinder. V = Л r 2 h V = Л4 2 (24) V = 384Л in 3

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 = h, where 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 units 3

9. Find the volume. Break it into smaller parts. V top = 10(2)(5) = 100 V bottom = 7(10)(4) = 280 Total Volume = 100 + 280 = 380 units 3