Pre-Algebra - Volume of a Cylinder

The area of the circular base of a cylinder is $4\pi$ . The height of the cylinder is . What is the volume of the cylinder?

$16\pi$

$4\pi +4$

$32\pi$

$64\pi$

$16\pi^2+4$

Explanation

Write the formula to find the volume of the cylinder.

$V=\pi r^2 h$

The $\pi r^2$ term represents the area of the circular base. Multiply the given area and the height to obtain the area.

$V=(4\pi)(4) = 16\pi$

Find the volume of a cylinder if the radius is 2 and the height is 12.

$48\pi$

$24\pi$

$12\pi$

$36\pi$

$15\pi$

Explanation

Write the volume formula for a cylinder.

$V=\pi r^2h$

Substitute the dimensions.

$V=\pi (2)^2(12) = 48\pi$

If Cindy has a cylindrical bucket filled with sand, how much sand does it contain if area of the circular bottom is $10\pi$ inches and the heigh of the bucket is inches?

$80\pi\ in^3$

$80\ in^3$

$800\pi\ in^3$

$40\pi\ in^3$

Explanation

To find the volume of a cylinder, the formula is $V = \pi r^{2} h$ .
Normally, you would simply input the radius given for "" and the height given for "". However, the question did not directly give us the radius; it gave us the area of the circular bottom.

Now examine the volume formula closely, and you will see that the formula for the area of a circle is hidden inside the volume formula. If $\pi r^{2}$ is the area of a circle, then we can simply multiply the area of the circle given by the height given.

V = area of the circle x height
$V=10\pi \times 8$
$V=80\pi$ cubed inches

What is the volume of a cylinder with a diameter equal to and height equal to ?

$72\pi$

$288\pi$

$144\pi$

$36\pi$

Explanation

If the diameter is 6, then the radius is half of 6, or 3.

Plug this radius into the formula for the volume of a cylinder:

$V=hr^2\pi=(8)(3^2)\pi=(8)(9)\pi=72\pi$

Find the volume of a cylinder with a base area of $\pi$ and a height of $\pi^2$ .

$\pi ^3$

$3\pi ^3$

$2\pi ^3$

$\pi^4$

$\frac{\pi^4}{4}$

Explanation

Write the formula to find the volume of the cylinder.

$V = \pi r^2 h = A_{\textup{circle}}h$

Because the base of the cylinder is a circle, the term $\pi r^2$ represents the area of the circular base, which is already given.

Multiply the area with the height to obtain the volume.

$V= \pi (\pi^2)=\pi ^3$

Find the volume of a cylinder with a diameter of 1 and a height of 2.

$\frac{1}{2}\pi$

$\frac{1}{4}\pi$

$\frac{1}{8}\pi$

$4\pi$

$2\pi$

Explanation

Write the formula for the volume of a cylinder.

$V=\pi r^2h$

Find the radius by dividing the diameter by 2.

$r=\frac{d}{2} = \frac{1}{2}$

$V=\pi (\frac{1}{2})^2(2)=\pi(\frac{1}{4})(2) = \frac{1}{2}\pi$

Find the volume of the cylinder.

Jared buys a can of chicken noodle soup for dinner. The height of the can is . The radius of the can is . What is the volume of the can?

$24\pi:in^3$

$12\pi:in^3$

$72\pi:in^3$

$6\pi:in^3$

$22\pi:in^3$

Explanation

The correct answer to the question is $24\pi:in^3$ .

We know that a can is a cylinder. We also know that the formula for the volume of a cylinder is $\pi r^{^{2}}h$ .

Plug in the numbers we are given:

$\pi \cdot 22 \cdot 6$

Once we multiply these numbers, we get $24\pi$ .

The unit for our answer is $in^{3}$ since we are solving a volume problem.

Find the volume of the cylinder if the base has a circumference of $4\pi$ and the height is 4.

$16\pi$

$4\pi$

$8\pi$

$32\pi$

Explanation

The base of a cylinder is a circle. Write the circumference formula.

$C=2\pi r$

Substitute the circumference and find the radius.

$4\pi=2\pi r$

Write the formula to find the volume for cylinders.

$V=\pi r^2h$

Substitute the dimensions.

$V=\pi (2)^2 (4) = 16\pi$

Solve for the volume of a cylindrical soda can if the base perimeter is $6\pi$ and the height is .

$54\pi$

$36\pi$

$18\pi$

$27\pi$

$108\pi$

Explanation

Write the formula for the volume of a cylinder.

$V=\pi r^2h$

The radius is unknown. In order to solve for the radius, use the base perimeter as a given to solve for the radius. The base perimeter is the circular circumference.

Write the formula for the circle's circumference.

$C=2\pi r$