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Pre-Algebra : Volume of a Cylinder

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Example Questions

Example Question #11 : Volume Of A Cylinder

Solve for the volume of a cylinder if the radius is and the height is twice the radius.

Possible Answers:

$1372\pi$

$441\pi$

$686 \pi$

$432\pi$

$196\pi$

Correct answer:

$686 \pi$

Explanation:

Write the formula for the volume of the cylinder.

$V=\pi r^2 h$

The height is 14, since it is twice the radius. Substitute the dimensions.

$\\V=\pi (7)^2 (14 ) \\V=\pi 49\cdot 14\\ V=686 \pi$

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Example Question #52 : Volume

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

Possible Answers:

$54\pi$

$27\pi$

$18\pi$

$108\pi$

$36\pi$

Correct answer:

$54\pi$

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.

$C=2\pi r$

Substitute the base perimeter.

$6\pi=2\pi r$

Divide $2\pi$ on both sides to solve for the radius.

$\frac{6\pi}{2\pi}=\frac{2\pi r}{2\pi}$

r=3

Substitute the radius and the height into the volume formula.

$V=\pi r^2h = \pi (3)^2 (6) = \pi (9)(6) =54\pi$

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Example Question #53 : Volume

You have a can of soup that looks like the following.

Volume2

The height is 5 in and the diameter is 4 in. If $\pi = 3.14$ , find the volume of the soup can. Round to the nearest tenths.

Possible Answers:

251.2in^2

125.6in^3

251.2in^3

62.8in^3

62.8in^2

Correct answer:

62.8in^3

Explanation:

The formula to find the volume of a cylinder is

$V = \pi r^2 h$

We know the diameter of the cylinder is 4in. The radius is half the diameter, so the radius of the cylinder is 2in. We know,

$\pi = 3.14$

$r = 2\text{in}$

$h = 5 \text{in}$

When we substitute into the formula, we get

$V = 3.14 * (2\text{in})^2 * 5\text{in}$

$V = 3.14 * 4\text{in}^2 * 5\text{in}$

$V = 62.8\text{in}^3$

Therefore, the volume of the soup can is $62.8\text{in}^3$

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Example Question #54 : Volume

A cylinder has a volume of $288\pi$ . If the height of the cylinder is , what is the radius?

Possible Answers:

Correct answer:

Explanation:

The formula for the volume of a cylinder is:

$V=\pi r^2h$

To find the radius, we simply plug in the given values and solve for :

$288\pi =\pi r^2(8)$

$\frac{288\pi}{\pi} =\frac{8\pi r^2}{\pi}$

288=8r^2

$\frac{288}{8}=\frac{8r^2}{8}$

36=r^2

$\sqrt{36}=\sqrt{r^2}$

6=r

Therefore, the radius of the circle is .

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Example Question #55 : Volume

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?

Possible Answers:

$80\ in^3$

$40\pi\ in^3$

$800\pi\ in^3$

$80\pi\ in^3$

Correct answer:

$80\pi\ in^3$

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

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Example Question #12 : Volume Of A Cylinder

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

Possible Answers:

$16\pi$

$32\pi$

$4\pi$

$8\pi$

Correct answer:

$16\pi$

Explanation:

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

$C=2\pi r$

Substitute the circumference and find the radius.

$4\pi=2\pi r$

r=2

Write the formula to find the volume for cylinders.

$V=\pi r^2h$

Substitute the dimensions.

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

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Pre-Algebra : Volume of a Cylinder

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #11 : Volume Of A Cylinder

Example Question #52 : Volume

Example Question #53 : Volume

Example Question #54 : Volume

Example Question #55 : Volume

Example Question #12 : Volume Of A Cylinder

All Pre-Algebra Resources

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