# High School Math : How to find the volume of a cylinder

## Example Questions

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### Example Question #1 : How To Find The Volume Of A Cylinder

What is the volume of a cylinder with a radius of 2 and a length that is three times as long as its diameter?

Explanation:

The volume of a cylinder is the base multiplied by the height or length.  The base is the area of a circle, which is .  Here, the radius is 2.  The diameter is 4. Three times the diameter is 12.  The height or length is 12. So, the answer is  .

### Example Question #2 : How To Find The Volume Of A Cylinder

A water glass has the shape of a right cylinder. The glass has an interior radius of 2 inches, and a height of 6 inches. The glass is 75% full. What is the volume of the water in the glass (in cubic inches)?

Explanation:

The volume of a right cylinder with radius  and height  is:

Since the glass is only 75% full, only 75% of the interior volume of the glass is occupied by water. Therefore the volume of the water is:

### Example Question #1 : How To Find The Volume Of A Cylinder

A circle has a circumference of  and it is used as the base of a cylinder. The cylinder has a surface area of . Find the volume of the cylinder.

Explanation:

Using the circumference, we can find the radius of the circle. The equation for the circumference is ; therefore, the radius is 2.

Now we can find the area of the circle using . The area is .

Finally, the surface area consists of the area of two circles and the area of the mid-section of the cylinder: , where  is the height of the cylinder.

Thus,  and the volume of the cylinder is .

### Example Question #2 : How To Find The Volume Of A Cylinder

What is the volume of a cylinder that has a base with a radius of 5 and a height of 52?

Explanation:

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

In this example the height is 52 and the radius is 5 which we plug into our equation which will look like this

We then square the 5 to get

Then perform multiplication to get

### Example Question #3 : How To Find The Volume Of A Cylinder

What is the surface area of a cylinder with a radius of 2 cm and a height of 10 cm?

40π cm2

48π cm2

36π cm2

32π cm2

56π cm2

48π cm2

Explanation:

SAcylinder = 2πrh + 2πr2 = 2π(2)(10) + 2π(2)2 = 40π + 8π = 48π cm2

### Example Question #4 : How To Find The Volume Of A Cylinder

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

Explanation:

In order to calculate the volume of a cylinder, we must utilize the formula . We were given the radius, , and the height, .

Insert the known variables into the formula and solve for volume .

In essence, we find the area of the cylinder's circular base, , and multiply it by the height.

### Example Question #5 : How To Find The Volume Of A Cylinder

A cylinder has a radius of  and a height of .  What is its volume

Not enough information to solve.

Explanation:

In order to calculate the volume of a cylinder, we must utilize the formula . We were given the radius, , and the height, .

Insert the known variables into the formula and solve for volume .

In essence, we find the area of the cylinder's circular base, , and multiply it by the height.

### Example Question #5 : How To Find The Volume Of A Cylinder

A sphere with a radius of  is circumscribed in a cylinder. What is the cylinder's volume?

Not enough information to solve

Explanation:

In order to solve this problem, one key fact needs to be understood.  A sphere will take up exactly  of the volume of a cylinder in which it is circumscribed. Therefore, if we find the volume of the sphere we can then solve for the volume of the cylinder.

First, we need to find the volume of the sphere.

This equals  of the volume of the cylinder. Therefore,

### Example Question #6 : How To Find The Volume Of A Cylinder

Calculate the volume of a cylinder with a height of six, and a base with a radius of three.

Explanation:

The volume of a cylinder is give by the equation .

In this example, and .

### Example Question #7 : How To Find The Volume Of A Cylinder

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

Explanation:

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

We then square the  to get

Then perform multiplication to get