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SSAT Upper Level Math : Volume of a Three-Dimensional Figure

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

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All SSAT Upper Level Math Resources

6 Diagnostic Tests 311 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

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

A given rectangular pyramid has a base length of $5\:m$ , a base width of $3\:m$ , and a height of $7\:m$ . What is the volume of the pyramid?

Possible Answers:

$35\:m^{3}$

$124\:m^3$

Cannot be determined with the information provided

$72\:m^3$

$105\:m^{3}$

Correct answer:

$35\:m^{3}$

Explanation:

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

$V=\frac{lwh}{3}$ .

Plugging in our given values for each variable, we have

$V=\frac{5\:m\times 3\:m\times 7\:m}{3}$

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

$V=5\:m\times1\:m\times7\:m$

$V=35\:m^{3}$

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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.

$\text{Volume}=\frac{\text{Area of base}\times height}{3}$

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

$\text{Area}=\text{length}\times\text{width}$

$\text{Area}=4\times3=12$

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.

$\text{Volume}=\frac{12\times7}{3}=\frac{84}{3}=28$

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

A rectangular pyramid has a length of 12m , a width of , and a height of . In cubic meters, what is the volume?

Possible Answers:

240

120

160

Correct answer:

Explanation:

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

$\text{Volume}=\frac{\text{Area of base}\times height}{3}$

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

$\text{Area}=\text{length}\times\text{width}$

$\text{Area}=12\times4=48$

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.

$\text{Volume}=\frac{48\times5}{3}=\frac{240}{3}=80$

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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 12m . In cubic meters, find the volume of the pyramid.

Possible Answers:

256

384

336

128

Correct answer:

128

Explanation:

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

$\text{Volume}=\frac{\text{Area of base}\times height}{3}$

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

$\text{Area}=\text{length}\times\text{width}$

$\text{Area}=4\times8=32$

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.

$\text{Volume}=\frac{32\times12}{3}=\frac{384}{3}=128$

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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 12m . In cubic meters, find the volume.

Possible Answers:

392

556

588

196

Correct answer:

196

Explanation:

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

$\text{Volume}=\frac{\text{Area of base}\times height}{3}$

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

$\text{Area}=\text{length}^2$

$\text{Area}=7^2=49$

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.

$\text{Volume}=\frac{49\times12}{3}=\frac{588}{3}=196$

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

A pyramid with a square base that has a side length of 12m has a height of . In cubic meters, find the volume.

Possible Answers:

480

240

720

960

Correct answer:

240

Explanation:

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

$\text{Volume}=\frac{\text{Area of base}\times height}{3}$

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

$\text{Area}=\text{length}^2$

$\text{Area}=12^2=144$

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.

$\text{Volume}=\frac{144\times4}{3}=\frac{720}{3}=240$

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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, what is the volume of the pyramid?

Possible Answers:

320

960

500

640

Correct answer:

320

Explanation:

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

$\text{Volume}=\frac{\text{Area of base}\times height}{3}$

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

$\text{Area}=\text{length}^2$

$\text{Area}=8^2=64$

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.

$\text{Volume}=\frac{64\times15}{3}=\frac{960}{3}=320$

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

A pyramid has a square base of side and a height of 11m . Find the volume of the pyramid in cubic meters.

Possible Answers:

132

264

396

256

Correct answer:

132

Explanation:

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

$\text{Volume}=\frac{\text{Area of base}\times height}{3}$

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

$\text{Area}=\text{length}^2$

$\text{Area}=6^2=36$

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.

$\text{Volume}=\frac{36\times11}{3}=\frac{396}{3}=132$

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Example Question #721 : Geometry

A pyramid has a square base of side and a height of 12m . In cubic meters, find the volume of the pyramid.

Possible Answers:

300

400

100

200

Correct answer:

100

Explanation:

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

$\text{Volume}=\frac{\text{Area of base}\times height}{3}$

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

$\text{Area}=\text{length}^2$

$\text{Area}=5^2=25$

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.

$\text{Volume}=\frac{25\times12}{3}=\frac{300}{3}=100$

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Example Question #722 : Geometry

A rectangular pyramid has a length of 15m , a width of , and a height of . In cubic meters, find the volume.

Possible Answers:

420

360

280

140

Correct answer:

140

Explanation:

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

$\text{Volume}=\frac{\text{Area of base}\times height}{3}$

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

$\text{Area}=\text{length}\times\text{width}$

$\text{Area}=15\times7=105$

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.

$\text{Volume}=\frac{105\times4}{3}=\frac{420}{3}=140$

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All SSAT Upper Level Math Resources

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SSAT Upper Level Math : Volume of a Three-Dimensional Figure

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

All SSAT Upper Level Math Resources

Example Questions

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

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

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

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

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

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

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

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

Example Question #721 : Geometry

Example Question #722 : Geometry

All SSAT Upper Level Math Resources

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