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

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #1 : Pyramids

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?

Possible Answers:

There is a 41% decrease 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

There is a 59% increase in volume

Correct answer:

There is a 41% 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 

 

The volume of the altered pyramid would be equal to:

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. 

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

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