How to find the length of an edge of a pyramid

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SAT Math › How to find the length of an edge of a pyramid

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If the height of a pyramid was increased by 20% and a side of the square base was decreased 30%, what would happen to the volume of the pyramid?

There is a 41% decrease in volume

There is a 59% increase in volume

It would have the same volume

59% decrease in volume

There is no way to know if it would increase or decrease in volume

Explanation

First, you will want to create a pyramid with measurements that are easy to calculate. So, let's say that we have pyramid with a base edge of 10 inches and a height of 10 inches.

So the volume of the original pyramid would be equal to

$\frac{(10\times 10)(10)}{3}=\frac{1000}{3}=333.33: inches^2$

The volume of the altered pyramid would be equal to:

$\frac{(7\times 7)(12)}{3}=\frac{588}{3}=196: inches^2$

To find the relationship between the volume of the altered pyramid relative to the volume of the original pyramid, divide the altered volume by the original volume.

$\frac{196}{333.33}=.59$

The new volume is 59% of the original volume, which means there was a 41% decrease in volume.