Volume of a Cylinder - Pre-Algebra

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Question

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

Answer

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:

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

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Question

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?

Answer

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.

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Question

A cylinder has a radius of 4 inches and a height of 5 inches. What is the volume of the cylinder?

Answer

The formula for the volume of the cylinder is $\small V=\pi r^2h$ , where $\small r$ is the radius and $\small h$ is the height. Plug in the lengths we are given to solve:

$\small V=\pi r^2h$

$\small V = \pi (4)^2(5)$

$\small V=\pi 16(5)$

$\small V = 80\pi$

The cylinder has a volume of $80\pi$ .

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Question

What is the volume of a cylinder with a height of 20 and a radius of 10?

Answer

The volume of a cylinder is given by the formula:

$\small \small volume=radius^2height\ast \pi$

with $\small height = 20$ and $\small radius = 10$ , the equation is:

$\small volume = 10^2 20\ast \pi$ ,

Thus, $\small volume = 100* 20\ast \pi$ , or $\small 2000\pi$

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Question

Find the volume of a cylinder that has a radius of 2 inches and a height of 10 inches.

$V = \pi r^2 * h$

Answer

Radius = 2 Inches

Height = 10

$V = \prod r^2 * h$

$V = \prod * 2^2 * 10$

$V = \prod * 40$

$V = 40\pi Inches^3$

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Question

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?

Answer

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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Question

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

Answer

Write the formula for the volume of a cylinder.

$V=\pi r^2h$

Find the radius by dividing the diameter by 2.

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

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

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Question

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?

Answer

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.

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

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Question

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

Answer

Write the volume formula for a cylinder.

$V=\pi r^2h$

Substitute the dimensions.

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

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Question

Find the volume of a cylinder with a radius and height of $2\pi$ .

Answer

Write the formula for the volume of a cylinder.

$V=\pi r^2h$

Substitute the dimensions.

$V=\pi (2\pi)^2(2\pi) = \pi(4\pi^2)(2\pi) = 8\pi^4$

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Question

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

Answer

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.

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

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Question

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

Answer

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.

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

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Question

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

Answer

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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Question

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

Answer

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.

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

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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Question

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

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.

Answer

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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Question

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

Answer

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 :

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

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

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

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

Therefore, the radius of the circle is .

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