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

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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?

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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}$$

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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?

Tap to reveal answer

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}$$

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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?

Tap to reveal answer

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:

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

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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?

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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?

Tap to reveal answer

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.

Tap to reveal answer

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.

Tap to reveal answer

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.

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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.

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.

Tap to reveal answer

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.

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?

Tap to reveal answer

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.

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.

Tap to reveal answer

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.

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.

Tap to reveal answer

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.

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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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?

Tap to reveal answer

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}$$

← Didn't Know|Knew It →

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?

Tap to reveal answer

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}$$

← Didn't Know|Knew It →

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?

Tap to reveal answer

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:

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

← Didn't Know|Knew It →

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?

Tap to reveal answer

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?

Tap to reveal answer

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.

Tap to reveal answer

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}$=128$

← Didn't Know|Knew It →

Question

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

Tap to reveal answer

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.

Tap to reveal answer

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.

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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