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

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Question

Can we determine the volume of this shape?

Answer

Volume is a characteristic of three-dimensional shapes. This is a cube, which is a three-dimensional shape. We can think of volume as space within an object or shape, so the volume would be the amount of space inside this cube.

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Question

Can we determine the volume of this shape?

Answer

Volume is a characteristic of three-dimensional shapes. This is a rectangular prism, which is a three-dimensional shape. We can think of volume as space within an object or shape, so the volume would be the amount of space inside this rectangular prism.

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Question

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

Answer

The volume of a given prism , where is the base area and is the height. For a rectangular prism, the base area $B=l \times w$ , or length times width. Therefore:

$V=(l\times w)h$

Substituting in our known values:

$V=(9:cm\times 5:cm)7:cm$

$V=45:cm^{2}\times 7:cm$

$V=315:cm^{3}$

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Question

Find the volume of a circular prism with a base radius of and a height of .

Answer

The volume of a given prism , where is the base area and is the height. For a circular prism, the base area $B=\pi r^{2}$ , or pi times the square of the radius. Therefore:

$V=(\pi r^{2})h$

Substituting in our known values:

$V=(\pi (11:cm)^{2})(20:cm)$

$V=(121\pi:cm^{2})(20:cm)$

$V=2420\pi:cm^{3}$

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Question

A triangular prism has a triangle base length of , a triangle height length of , and a prism height of . What is the volume of the prism?

Answer

The volume of a given prism , where is the base area and is the prism height. For a triangular prism, the base area $B=\frac{1}{2}bh_{2}$ , where is the base of the triangle and $h_{2}$ is the height of the triangle (not of the prism).

Therefore, we can substitute the base area equation into the equation for the volume of a prism:

$V=(\frac{1}{2}bh_{2})h$

Substituting in our known values:

$V=(\frac{1}{2}(4:cm)(8:cm))(12:cm)$

$V=(16:cm^{2})(12:cm)$

$V=192:cm^{3}$

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Question

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

Answer

The volume of a rectangular prism is the product of its base area and its height : . Since we can determine the base area of the rectangular prism from its length and width, we can rewrite the equation and solve:

$V=12 \times48$

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Question

Can we determine the volume of this shape?

Answer

Volume is a characteristic of three-dimensional shapes. This is a cube, which is a three-dimensional shape. We can think of volume as space within an object or shape, so the volume would be the amount of space inside this cube.

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Question

A given rectangular prism has a length of , a width of , and a height of , what is its volume?

Answer

The volume of a rectangular prism is the product of its base area and its height : . Since we can determine the base area of the rectangular prism from its length and width, we can rewrite the equation and solve:

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Question

What is the volume of the shape below?

Answer

The formula for volume of a rectangular prism is $\small v=l\times w\times h$

$\small v=3\times1\times2$

$\small v=6cm^3$

Remember, volume is always labeled as units to the third power.

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Question

What is the volume of the shape below?

Answer

The formula for volume of a rectangular prism is $\small v=l\times w\times h$

$\small v=6\times3\times2$

$\small v=36cm^3$

Remember, volume is always labeled as units to the third power.

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Question

What is the volume of the shape below?

Answer

The formula for volume of a rectangular prism is $\small v=l\times w\times h$

$\small v=6\times3\times6$

$\small v=108cm^3$

Remember, volume is always labeled as units to the third power.

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Question

Can we determine the volume of this shape?

Answer

Volume is a characteristic of three-dimensional shapes. This is a cylinder, which is a three-dimensional shape. We can think of volume as space within an object or shape, so the volume would be the amount of space inside this cylinder.

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Question

What is the volume of the shape below?

Answer

The formula for volume of a rectangular prism is $\small v=l\times w\times h$

$\small v=8\times4\times6$

$\small v=192cm^3$

Remember, volume is always labeled as units to the third power.

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Question

What is the volume of the shape below?

Answer

The formula for volume of a rectangular prism is $\small v=l\times w\times h$

$\small v=2\times3\times7$

$\small v=42cm^3$

Remember, volume is always labeled as units to the third power.

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Question

What is the volume of the shape below?

Answer

The formula for volume of a rectangular prism is $\small v=l\times w\times h$

$\small v=3\times4\times7$

$\small v=84cm^3$

Remember, volume is always labeled as units to the third power.

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Question

What is the volume of the shape below?

Answer

The formula for volume of a rectangular prism is $\small v=l\times w\times h$

$\small v=10\times9\times11$

$\small v=990in^3$

Remember, volume is always labeled as units to the third power.

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Question

Can we determine the volume of this shape?

Answer

Volume is a characteristic of three-dimensional shapes. This is a cylinder, which is a three-dimensional shape. We can think of volume as space within an object or shape, so the volume would be the amount of space inside this cylinder.

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Question

What is the volume of the shape below?

Answer

The formula for volume of a rectangular prism is $\small v=l\times w\times h$

$\small v=13\times\7\times11$

$\small v=1,001in^3$

Remember, volume is always labeled as units to the third power.

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Question

What is the volume of the shape below?

Answer

The formula for volume of a rectangular prism is $\small v=l\times w\times h$

$\small v=13\times5\times15$

$\small v=975in^3$

Remember, volume is always labeled as units to the third power.

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Question

What is the volume of the shape below?

Answer

The formula for volume of a rectangular prism is $\small v=l\times w\times h$

$\small v=13\times7\times12$

$\small v=1,092in^3$

Remember, volume is always labeled as units to the third power.

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