How to find the volume of a cylinder in pre-algebra - Math

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Question

What is the radius of a cylinder with a volume of $128\pi$ and a height of ?

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Answer

When you think of volume, think of it as a stack of something. A cube is a stack of squares. A cylinder is a stack of circles. That means that the volume of a cylinder will be the area of that circle times the height, or $V=(\pi r^2)h$ .

Plug in our given values to solve:

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

$128\pi=(\pi r^2)*8$

Divide both sides by .

$\frac{128\pi}{8}=\pi r^2$

$16\pi=\pi r^2$

Divide both sides by $\pi$ .

Take the square root of both sides:

$\sqrt{16}=\sqrt{r^2}$

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Question

What is the volume of a cylinder with a circular side with a radius of and a length of ?

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Answer

To find the volume of a cylinder we must know the equation for the volume of a cylinder which is

In this example the length is and the radius is so our equation will look like this $Volume=\pi(6^{2})(12)$

We then square the to get .

Then perform multiplication to get $432\pi$ .

The answer is $432\pi$ .

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Question

What is the volume of a cylinder with a circle radius of and a length of ?

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Answer

To find the volume of a cylinder we must know the equation for the volume of a cylinder which is .

Here the length is and the radius is , so the equation becomes $V=(8^{2})(14)(\pi)$ .

First square the to get $8^{2}=64$ .

Then perform multiplication to get $(64)(14)(\pi)=896\pi$ .

The answer is therefore $896\pi$ .

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Question

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

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Answer

When you think of volume, think of it as a stack of something. A cube is a stack of squares. A cylinder is a stack of circles. That means that the volume of a cylinder will be the area of that circle times the height, or $V=(\pi r^2)h$

Plug in our given numbers to solve:

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

$V=(\pi 2^2)9$

$V=4\pi9$

$V=36\pi$

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Question

What is the radius of a cylinder with a volume of $144\pi$ and a height of ?

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Answer

When you think of volume, think of it as a stack of something. A cube is a stack of squares. A cylinder is a stack of circles. That means that the volume of a cylinder will be the area of that circle times the height, or $V=(\pi r^2)h$ .

Plug in our given values to solve:

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

$144\pi=(\pi r^2)*9$

Divide both sides by .

$\frac{144\pi}{9}=\pi r^2$

$16\pi=\pi r^2$

Divide both sides by $\pi$ .

Take the square root of both sides:

$\sqrt{16}=\sqrt{r^2}$

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Question

What is the height of a cylinder with a volume of $384\pi$ and a radius of ?

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Answer

When you think of volume, think of it as a stack of something. A cube is a stack of squares. A cylinder is a stack of circles. That means that the volume of a cylinder will be the area of that circle times the height, or $V=(\pi r^2)h$ .

Plug in our given values to solve:

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

$384\pi=(\pi 8^2)h$

$384\pi=64\pih$

Divide both sides by $64\pi$ :

$\frac{384\pi}{64\pi}=h$

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Question

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

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Answer

When you think of volume, think of it as a stack of something. A cube is a stack of squares. A cylinder is a stack of circles. That means that the volume of a cylinder will be the area of that circle times the height, or $V=(\pi r^2)h$ .

Plug in our given values to solve:

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

$V=(\pi 3^2)7$

$V=9\pi7$

$V=63\pi$

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Question

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

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Answer

When you think of volume, think of it as a stack of something. A cube is a stack of squares. A cylinder is a stack of circles. That means that the volume of a cylinder will be the area of that circle times the height, or $V=(\pi r^2)h$ .

Plug in our given values to solve:

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

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

$V=25\pi2$

$V=50\pi$

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Question

What is the volume of a cylinder with a circle radius of and a length of ?

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Answer

To find the volume of a cylinder we must know the equation for the volume of a cylinder, which is .

In this example, the length is and the radius is , so our equation will look like this: $V=(8^{2})(21)(\pi)$

We then square the to get $8^{2}=64$ .

Then perform multiplication to get $V=1344\pi$ .

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Question

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

Tap to reveal answer

Answer

When thinking about volume, think of it as a stack of something. In this case, a cylinder is a stack of circles. We want the area of the bottom circle times the height, or $V=(\pi r^2)h$ .

Plug in our given information and solve:

$V=(\pi3^2)6$

$V=9\pi6$

$V=54\pi$

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Question

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

Tap to reveal answer

Answer

When thinking about volume, think of it as a stack of something. In this case, a cylinder is a stack of circles. We want the area of the bottom circle times the height, or $V=(\pi r^2)h$ .

Plug in and solve:

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

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

$V=16\pi5$

$V=80\pi$

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Question

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

Tap to reveal answer

Answer

When thinking about volume, think of it as a stack of something. In this case, a cylinder is a stack of circles. We want the area of the bottom circle times the height, or $V=(\pi r^2)h$ .

Plug in and solve:

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

$V=(\pi 2^2)10$

$V=4\pi10$

$V=40\pi$

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Question

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

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Answer

The formula for the volume of a cylinder is the area of the base circle times the height, or $V=\pi r^2h$ .

Plug in our given info to solve.

$V=\pi r^2h$

$V=\pi 10^210$

$V=100\pi10$

$V=1000\pi$

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Question

What is the volume of a cone with a circle radius of and a height of ?

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Answer

To find the volume of a cone we must use the equation

We must first solve for the area of the circle using .

The equation for the area of a circle is

We plug in and square it to get

$A=49\pi$

We then plug our answer into the equation for the cone with to get

$V=\frac{1}{3}\cdot (49\pi)\cdot (24)$

We multiply to get our final answer for the volume of the cone

$V=392\pi$

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Question

What is the volume of a cylinder with a circular side with a radius of and a length of ?

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Answer

To find the volume of a cylinder we must know the equation for the volume of a cylinder which is

In this example the length is and the radius is so our equation will look like this

$V=7^{2}(\pi)(44)$

We then square the to get

$V=(49)(\pi)(44)$

Then perform multiplication to get $V=2156\pi$ .

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Question

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

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Answer

To find the volume of a cylinder, use the equation:

$Volume=\pi\cdot\ Radius^{2}\cdot\ Height$

Substitute the given values for radius and height:

$Volume=\pi\cdot(17^{2})\cdot21$

$Volume=\pi \cdot 289\cdot 21$

$Volume=6069\pi$

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Question

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

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Answer

The formula for the volume of a cylinder is $V = \pi r^{2}h$ , where is the radius, and is the height.

Plugging into this formula with our given values, we see that $V = \pi (3)^{2}(5) = \pi (9)(5) = 45\pi$ inches cubed.

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Question

What is the radius of a cylinder with a volume of $128\pi$ and a height of ?

Tap to reveal answer

Answer

When you think of volume, think of it as a stack of something. A cube is a stack of squares. A cylinder is a stack of circles. That means that the volume of a cylinder will be the area of that circle times the height, or $V=(\pi r^2)h$ .

Plug in our given values to solve:

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

$128\pi=(\pi r^2)*8$

Divide both sides by .

$\frac{128\pi}{8}=\pi r^2$

$16\pi=\pi r^2$

Divide both sides by $\pi$ .

Take the square root of both sides:

$\sqrt{16}=\sqrt{r^2}$

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Question

What is the volume of a cylinder with a circular side with a radius of and a length of ?

Tap to reveal answer

Answer

To find the volume of a cylinder we must know the equation for the volume of a cylinder which is

In this example the length is and the radius is so our equation will look like this $Volume=\pi(6^{2})(12)$

We then square the to get .

Then perform multiplication to get $432\pi$ .

The answer is $432\pi$ .

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Question

What is the volume of a cylinder with a circle radius of and a length of ?

Tap to reveal answer

Answer

To find the volume of a cylinder we must know the equation for the volume of a cylinder which is .

Here the length is and the radius is , so the equation becomes $V=(8^{2})(14)(\pi)$ .

First square the to get $8^{2}=64$ .

Then perform multiplication to get $(64)(14)(\pi)=896\pi$ .

The answer is therefore $896\pi$ .

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