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

Card 0 of 20

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:

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

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

$V=315:cm^{3}$

Compare your answer with the correct one above

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:

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

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

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

Compare your answer with the correct one above

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:

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

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

$V=192:cm^{3}$

Compare your answer with the correct one above

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:

$V=12 \times48$

Compare your answer with the correct one above

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:

Compare your answer with the correct one above

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.

Compare your answer with the correct one above

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.

Compare your answer with the correct one above

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.

Compare your answer with the correct one above

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.

Compare your answer with the correct one above

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.

Compare your answer with the correct one above

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.

Compare your answer with the correct one above

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.

Compare your answer with the correct one above

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.

Compare your answer with the correct one above

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.

Compare your answer with the correct one above

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.

Compare your answer with the correct one above

Question

What is the volume of the shape below?

Answer

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

$\small v=5\times6\times18$

$\small v=540in^3$

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

Compare your answer with the correct one above

Question

What is the volume of the shape below?

Answer

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

$\small v=6\times6\times20$

$\small v=\small 720in^2$

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

Compare your answer with the correct one above

Question

What is the volume of the object below?

Answer

This object has $\small 2$ rows with $\small 3$ cubes in each row. We can multiply to find the volume.

$\small 2\times3=6$

$\small \small v=6\ units^3$

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

Compare your answer with the correct one above

Question

What is the volume of the object below?

Answer

This object has $\small 2$ rows with $\small 2$ cubes in each row. We can multiply to find the volume.

$\small 2\times2=4$

$\small v=4\ units^3$

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

Compare your answer with the correct one above

Question

What is the volume of the object below?

Answer

This object has rows with cubes in each row. We can multiply to find the volume.

$3\times2=6$

$v=6\ units^3$

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

Compare your answer with the correct one above

Tap the card to reveal the answer