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

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #651 : Geometry

The volume of a cylinder is  units cubed. If the cylinder's height is  units, what is its radius?

Possible Answers:

 units

 units

 units

 units

Correct answer:

 units

Explanation:

The formula for the volume of a cylinder is , where  is volume,  is the radius of the cylinder, and  is its height. Substituing the given information into this equation makes it possible to find the radius by solving for :

 units

Example Question #12 : How To Find The Volume Of A Cylinder

This figure is a right cylinder with radius of 2 m and a height of 10 m.Cylinder

What is the volume of the right cylinder (m3)?

Possible Answers:

Correct answer:

Explanation:

The formula for the volume of a right cylinder is  where  is the radius and  is the height.  Thus for this problem 

Example Question #13 : How To Find The Volume Of A Cylinder

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

Possible Answers:

Correct answer:

Explanation:

When thinking of a 3D figure, think of it as a stack of something. In this case, a cylinder is a stack of a circles.

The volume will be the area of that base circle times the height of the cylinder. Mathematically that would be .

Plug in our given values and solve.

Example Question #14 : How To Find The Volume Of A Cylinder

Find the volume of a cylinder given that its height and radius are 4 and 11, respectively. 

Possible Answers:

Correct answer:

Explanation:

The standard equation to find the volume of a cylinder is 

where  denotes height and  denotes radius.

Plug in the given values for height and radius to find the volume of the cylinder:

Example Question #23 : Cylinders

Find the volume of the following cylinder.

Cylinder

Possible Answers:

Correct answer:

Explanation:

The formula for the volume of a cylinder is:

where  is the radius of the base and  is the length of the height.

 

Plugging in our values, we get:

Example Question #24 : Cylinders

Find the volume of the following cylinder.

Cylinder

Possible Answers:

Correct answer:

Explanation:

The formula for the volume of a cylinder is:

Where  is the radius of the base and  is the height of the cylinder

 

Plugging in our values, we get:

Example Question #15 : How To Find The Volume Of A Cylinder

Find the volume of the following partial cylinder.

Cylinder_sector

Possible Answers:

Correct answer:

Explanation:

The formula for the volume of a partial cylinder is:

Where  is the radius of the cylinder,  is the height of the cylinder, and  is the degrees of the sector.

 

Plugging in our values, we get:

Example Question #121 : Solid Geometry

Find the volume of the following partial cylinder.

Partial_cylinder

Possible Answers:

Correct answer:

Explanation:

The formula for the volume of a partial cylinder is:

where  is the radius of the cylinder,  is the height of the cylinder, and  is the degrees of the sector.

 

Plugging in our values, we get:

Example Question #11 : How To Find The Volume Of A Cylinder

If a cylinder has a radius, \small r, of 2 inches and a height, \small h, of 5 inches, what is the total surface area of the cylinder?

Possible Answers:

\small 28\pi

\small 18\pi

\small 70\pi

\small 24\pi

\small 36\pi

Correct answer:

\small 28\pi

Explanation:

The total surface area will be equal to the area of the two bases added to the area of the outer surface of the cylinder. If "unwrapped" the area of the outer surface is simply a rectangle with the height of the cylinder and a base equal to the circumference of the cylinder base. We can use these relationships to find a formula for the total area of the cylinder.

Use the given radius and height to solve for the final area.

\small 2\pi(2)^{2} + 2\pi (2)(5)

\small 8\pi + 20\pi

\small 28\pi

Example Question #1042 : Act Math

The volume of a cylinder is . If the radius of the cylinder is , what is the surface area of the cylinder?

Possible Answers:

Correct answer:

Explanation:

The volume of a cylinder is equal to:

Use this formula and the given radius to solve for the height.

Now that we know the height, we can solve for the surface area. The surface area of a cylinder is equal to the area of the two bases plus the area of the outer surface. The outer surface can be "unwrapped" to form a rectangle with a height equal to the cylinder height and a base equal to the circumference of the cylinder base. Add the areas of the two bases and this rectangle to find the total area.

Use the radius and height to solve.

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