How to find the volume of a pyramid - SSAT Upper Level Quantitative (Math)

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Question

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?

Answer

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

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

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

$V=125000:m^{3}$

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Question

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?

Answer

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

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

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

$V=84000:m^{3}$

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Question

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

Answer

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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Question

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

Answer

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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Question

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

Answer

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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Question

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

Answer

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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Question

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

Answer

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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Question

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

Answer

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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Question

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

Answer

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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Question

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?

Answer

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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Question

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

Answer

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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Question

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

Answer

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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