Question

Amy and Alex are making models for their science project. Both the models are in the shape of a square pyramid. The length of the sides of the base for both the models is 8 inches. Amy’s model is 5 inches tall and Alex’s model is 3 inches tall. Find the difference in volume of the two models.

Answer 1

The difference in volume of the two models is
`(128)/(3)\ in^(3)`

Explanation:

we know that

The volume of a square pyramid is equal to

`V=(1)/(3)b^(2)h`

where

b is the length of the side of the square base

h is the height of the pyramid

step 1

Find the volume of Amy's model

we have

`b=8\ in`

`h=5\ in`

substitute

`V=(1)/(3)(8)^(2)(5)`

`V=(320)/(3)\ in^(3)`

step 2

Find the volume of Alex's model

we have

`b=8\ in`

`h=3\ in`

substitute

`V=(1)/(3)(8)^(2)(3)`

`V=(192)/(3)\ in^(3)`

step 3

Find the difference in volume of the two models

`(320)/(3)\ in^(3)-(192)/(3)\ in^(3)=(128)/(3)\ in^(3)`