Question

Explain the relationship between the volumes of a square pyramid and a rectangular prism if they each have a square bass with side length of 5 inches and they each have a height oh h inches.

Answer 1

The volume of the pyramid is one third the volume of the rectangular prism

or

The volume of the prism is three times the volume of the pyramid

Explanation:

step 1

Find the volume of the rectangular prism

The volume is equal to

`V=Bh`

where

B is the area of the base

h is the height of the prism

Find the area of the base B

`B=5^(2)=25\ in^(2)`

substitute

`Vprism=25h\ in^(3)`

step 2

Find the volume of the square pyramid

The volume is equal to

`V=(1/3)Bh`

where

B is the area of the base

h is the height of the pyramid

Find the area of the base B

`B=5^(2)=25\ in^(2)`

substitute

`Vpyramid=(1/3)25h\ in^(3)`

Remember that

`Vprism=25h\ in^(3)`

substitute

`Vpyramid=(1/3)Vprism`

The volume of the pyramid is one third the volume of the rectangular prism

or

`Vprism=3Vpyramid`

The volume of the prism is three times the volume of the pyramid