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

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Example Questions

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

A given right rectangular pyramid has a base length and base width of $60\:m$ $\displaystyle 60\:m$ , as well as a height of $70\:m$ $\displaystyle 70\:m$ . What is the volume of the pyramid?

Possible Answers:

$84000\:m^{3}$ $\displaystyle 84000\:m^{3}$

Not enough information provided

$252,000\:m^{3}$ $\displaystyle 252,000\:m^{3}$

$364,500\:m^{3}$ $\displaystyle 364,500\:m^{3}$

$124,000\:m^3$ $\displaystyle 124,000\:m^3$

Correct answer:

$84000\:m^{3}$ $\displaystyle 84000\:m^{3}$

Explanation:

The volume $\displaystyle V$ of a right rectangular pyramid with base length $\displaystyle l$ , base width $\displaystyle w$ , and height $\displaystyle h$ can be determined with the following formula:

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

Plugging in our given values for each variable, we have

$V=\frac{60\:m\times 60\:m\times 70\:m}{3}$ $\displaystyle V=\frac{60\:m\times 60\:m\times 70\:m}{3}$

$V=\frac{252000\:m^{3}}{3}$ $\displaystyle V=\frac{252000\:m^{3}}{3}$

$V=84000\:m^{3}$ $\displaystyle V=84000\:m^{3}$

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

A given right rectangular pyramid has a base length of $100\:m$ $\displaystyle 100\:m$ , a base width of $50\:m$ $\displaystyle 50\:m$ , and a height of $75\:m$ $\displaystyle 75\:m$ . What is the volume of the pyramid?

Possible Answers:

$225\:m^{3}$ $\displaystyle 225\:m^{3}$

$375,000\:m^{2}$ $\displaystyle 375,000\:m^{2}$

$125,000\:m^{3}$ $\displaystyle 125,000\:m^{3}$

$125,000\:m^{2}$ $\displaystyle 125,000\:m^{2}$

$375,000\:m^{3}$ $\displaystyle 375,000\:m^{3}$

Correct answer:

$125,000\:m^{3}$ $\displaystyle 125,000\:m^{3}$

Explanation:

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

Plugging in our given values for each variable, we have

$V=\frac{100\:m\times 50\:m\times 75\:m}{3}$ $\displaystyle V=\frac{100\:m\times 50\:m\times 75\:m}{3}$

$V=\frac{375000\:m^{3}}{3}$ $\displaystyle V=\frac{375000\:m^{3}}{3}$

$V=125000\:m^{3}$ $\displaystyle V=125000\:m^{3}$

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

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

Possible Answers:

$35\:m^{3}$ $\displaystyle 35\:m^{3}$

$124\:m^3$ $\displaystyle 124\:m^3$

Cannot be determined with the information provided

$72\:m^3$ $\displaystyle 72\:m^3$

$105\:m^{3}$ $\displaystyle 105\:m^{3}$

Correct answer:

$35\:m^{3}$ $\displaystyle 35\:m^{3}$

Explanation:

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

Plugging in our given values for each variable, we have

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

In this instance, since we have a $\displaystyle 3$ in both the numerator and the denominator, we can reduce the formula to:

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

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

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

A rectangular pyramid has a width of $\displaystyle 4m$ , a height of $\displaystyle 7m$ , and a length of $\displaystyle 3m$ . What is the volume of this pyramid, in cubic meters?

Possible Answers:

$\displaystyle 84$

$\displaystyle 36$

$\displaystyle 28$

$\displaystyle 48$

Correct answer:

$\displaystyle 28$

Explanation:

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

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

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

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

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

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.

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

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

A rectangular pyramid has a length of 12m $\displaystyle 12m$ , a width of $\displaystyle 4m$ , and a height of $\displaystyle 5m$ . In cubic meters, what is the volume?

Possible Answers:

240 $\displaystyle 240$

120 $\displaystyle 120$

$\displaystyle 80$

160 $\displaystyle 160$

Correct answer:

$\displaystyle 80$

Explanation:

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

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

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

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

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

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.

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

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Example Question #101 : Volume Of A Three Dimensional Figure

A rectangular pyramid has a length of $\displaystyle 4m$ , a width of $\displaystyle 8m$ , and a height of 12m $\displaystyle 12m$ . In cubic meters, find the volume of the pyramid.

Possible Answers:

256 $\displaystyle 256$

128 $\displaystyle 128$

336 $\displaystyle 336$

384 $\displaystyle 384$

Correct answer:

128 $\displaystyle 128$

Explanation:

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

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

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

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

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

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.

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

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Example Question #102 : Volume Of A Three Dimensional Figure

A pyramid has a square base with a side length of $\displaystyle 7m$ and a height of 12m $\displaystyle 12m$ . In cubic meters, find the volume.

Possible Answers:

196 $\displaystyle 196$

556 $\displaystyle 556$

588 $\displaystyle 588$

392 $\displaystyle 392$

Correct answer:

196 $\displaystyle 196$

Explanation:

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

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

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

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

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

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.

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

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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 $\displaystyle 12m$ has a height of $\displaystyle 5m$ . In cubic meters, find the volume.

Possible Answers:

480 $\displaystyle 480$

240 $\displaystyle 240$

720 $\displaystyle 720$

960 $\displaystyle 960$

Correct answer:

240 $\displaystyle 240$

Explanation:

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

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

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

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

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

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.

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

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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 $\displaystyle 8m$ has a height of $\displaystyle 15$ $\displaystyle m$ . In cubic meters, what is the volume of the pyramid?

Possible Answers:

320 $\displaystyle 320$

960 $\displaystyle 960$

500 $\displaystyle 500$

640 $\displaystyle 640$

Correct answer:

320 $\displaystyle 320$

Explanation:

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

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

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

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

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

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.

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

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

A pyramid has a square base of side $\displaystyle 6m$ and a height of 11m $\displaystyle 11m$ . Find the volume of the pyramid in cubic meters.

Possible Answers:

132 $\displaystyle 132$

264 $\displaystyle 264$

396 $\displaystyle 396$

256 $\displaystyle 256$

Correct answer:

132 $\displaystyle 132$

Explanation:

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

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

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

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

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

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.

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

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

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 #2 : How To Find The Volume Of A Pyramid

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 #101 : Volume Of A Three Dimensional Figure

Example Question #102 : Volume Of A Three Dimensional Figure

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

All SSAT Upper Level Math Resources

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