Volume of a Cylinder - Pre-Algebra

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

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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:

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?

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The correct answer to the question is .

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 since we are solving a volume problem.

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

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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 $80\pi$ .

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

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The volume of a cylinder is given by the formula:

$\small \small $volume=radius^2$height\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 $\small 2000\pi$

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

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

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Radius = 2 Inches

Height = 10

$V = \prod $r^2$ * h$

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

$V = \prod * 40$

$V = 40\pi $Inches^3$$

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?

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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

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

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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$

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?

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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.

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Write the volume formula for a cylinder.

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

Substitute the dimensions.

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

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

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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$$

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

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

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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 cylinder if the radius is and the height is twice the radius.

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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$

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

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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$

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.

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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

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

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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}$

Therefore, the radius of the circle is .

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

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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:

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?

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The correct answer to the question is .

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 since we are solving a volume problem.

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

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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 $80\pi$ .

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

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The volume of a cylinder is given by the formula:

$\small \small $volume=radius^2$height\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 $\small 2000\pi$