SSAT Upper Level Math : How to find the volume of a pyramid

Study concepts, example questions & explanations for SSAT Upper Level Math

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Example Questions

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Example Question #1 : How To Find The Volume Of A Pyramid

A given right rectangular pyramid has a base length and base width of , as well as a height of . What is the volume of the pyramid?

Possible Answers:

Not enough information provided

Correct answer:

Explanation:

The volume  of a right rectangular pyramid with base length , base width , and height  can be determined with the following formula:

.

Plugging in our given values for each variable, we have

Example Question #2 : How To Find The Volume Of A Pyramid

A given right rectangular pyramid has a base length of , a base width of , and a height of . What is the volume of the pyramid?

Possible Answers:

Correct answer:

Explanation:

The volume  of a right rectangular pyramid with base length , base width , and height  can be determined with the following formula:

.

Plugging in our given values for each variable, we have

Example Question #3 : How To Find The Volume Of A Pyramid

A given rectangular pyramid has a base length of , a base width of , and a height of . What is the volume of the pyramid?

Possible Answers:

Cannot be determined with the information provided

Correct answer:

Explanation:

The volume  of a right rectangular pyramid with base length , base width , and height  can be determined with the following formula:

.

Plugging in our given values for each variable, we have

In this instance, since we have a  in both the numerator and the denominator, we can reduce the formula to:

Example Question #4 : How To Find The Volume Of A Pyramid

A rectangular pyramid has a width of , a height of , and a length of . What is the volume of this pyramid, in cubic meters?

Possible Answers:

Correct answer:

Explanation:

Use the following formula to find the volume of a pyramid.

Since we have a rectangular pyramid, the base of the pyramid is a rectangle. Find the area of the rectangle.

Now, plug in the value for the area of the base and the height into the volume formula to find the volume of the pyramid.

 

Example Question #5 : How To Find The Volume Of A Pyramid

A rectangular pyramid has a length of , a width of , and a height of . In cubic meters, what is the volume?

Possible Answers:

Correct answer:

Explanation:

Use the following formula to find the volume of a pyramid.

Since we have a rectangular pyramid, the base of the pyramid is a rectangle. Find the area of the rectangle.

Now, plug in the value for the area of the base and the height into the volume formula to find the volume of the pyramid.

 

Example Question #6 : How To Find The Volume Of A Pyramid

A rectangular pyramid has a length of , a width of , and a height of . In cubic meters, find the volume of the pyramid.

Possible Answers:

Correct answer:

Explanation:

Use the following formula to find the volume of a pyramid.

Since we have a rectangular pyramid, the base of the pyramid is a rectangle. Find the area of the rectangle.

Now, plug in the value for the area of the base and the height into the volume formula to find the volume of the pyramid.

 

Example Question #7 : How To Find The Volume Of A Pyramid

A pyramid has a square base with a side length of  and a height of . In cubic meters, find the volume.

Possible Answers:

Correct answer:

Explanation:

Use the following formula to find the volume of a pyramid.

Since we have a square pyramid, the base of the pyramid is a square. Find the area of the square.

Now, plug in the value for the area of the base and the height into the volume formula to find the volume of the pyramid.

 

Example Question #8 : How To Find The Volume Of A Pyramid

A pyramid with a square base that has a side length of  has a height of . In cubic meters, find the volume.

Possible Answers:

Correct answer:

Explanation:

Use the following formula to find the volume of a pyramid.

Since we have a square pyramid, the base of the pyramid is a square. Find the area of the square.

Now, plug in the value for the area of the base and the height into the volume formula to find the volume of the pyramid.

 

Example Question #9 : How To Find The Volume Of A Pyramid

A pyramid with a square base that has a side length of  has a height of . In cubic meters, what is the volume of the pyramid?

Possible Answers:

Correct answer:

Explanation:

Use the following formula to find the volume of a pyramid.

Since we have a square pyramid, the base of the pyramid is a square. Find the area of the square.

Now, plug in the value for the area of the base and the height into the volume formula to find the volume of the pyramid.

 

Example Question #10 : How To Find The Volume Of A Pyramid

A pyramid has a square base of side  and a height of . Find the volume of the pyramid in cubic meters.

Possible Answers:

Correct answer:

Explanation:

Use the following formula to find the volume of a pyramid.

Since we have a square pyramid, the base of the pyramid is a square. Find the area of the square.

Now, plug in the value for the area of the base and the height into the volume formula to find the volume of the pyramid.

 

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