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

Answer:

The difference in volume of the two models is $\frac{128}{3}\ in^{3}$

Step-by-step explanation:

we know that

The volume of a square pyramid is equal to

$V=\frac{1}{3}b^{2}h$

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

$V=\frac{1}{3}(8)^{2}(5)$

$V=\frac{320}{3}\ in^{3}$

step 2

Find the volume of Alex's model

we have

$b=8\ in$

$h=3\ in$

substitute

$V=\frac{1}{3}(8)^{2}(3)$

$V=\frac{192}{3}\ in^{3}$

step 3

Find the difference in volume of the two models

$\frac{320}{3}\ in^{3}-\frac{192}{3}\ in^{3}=\frac{128}{3}\ in^{3}$