Take note Theorem 11-5: Cavalieri's Principle

If two space figures have the same height and the same cross-sectional area at every level, then they have the same volume.

Take note Theorem 11-6: Volume of a Prism

The volume of a prism is the product of the area of the base and the height of the prism.

V = B h v equals b h

Problem 1 Finding the Volume of a Rectangular Prism

What is the volume of the rectangular prism below?

V = B h Use the formula for the volume of a prism.   = 480 · 10 The area of the base  B  is  24 · 20 ,  or  480  cm 2 , and the height is 10  cm.   = 4800 Simplify. table with 3 rows and 4 columns , row1 column 1 , v , column 2 equals , column 3 b h , column 4 cap use the formula for the volume of a prism. , row2 column 1 , , column 2 equals , column 3 480 middle dot 10 , column 4 table with 2 rows and 1 column , row1 column 1 , cap the area of the base b , is , 24 middle dot 20 comma , or , 480 , cm squared , comma , row2 column 1 , and the height is . 10 , cm. , end table , row3 column 1 , , column 2 equals , column 3 4800 , column 4 cap simplify. , end table

The volume of the rectangular prism is 4800 cm 3 . 4800 . cm cubed , .

✓ Got It?

1. 1. What is the volume of the rectangular prism below?

      

   2. Reasoning Suppose the prism above is turned so that the base is 4 ft by 5 ft and the height is 3 ft. Does the volume change? Explain.