Intermediate Geometry : How to find the volume of a cylinder

Study concepts, example questions & explanations for Intermediate Geometry

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Example Questions

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Example Question #60 : Cylinders

Inscribed

The above diagram shows a sphere inscribed inside a cylinder.

The sphere has a volume of 100. Give the volume of the cylinder.

Possible Answers:

Correct answer:

Explanation:

Let  be the radius of the sphere. Then the radius of the base of the cylinder is also , and the height of the cylinder is .

The volume of the cylinder is

,

which, after substituting, is

The volume of the sphere is 

Therefore, the ratio of the former to the latter is

and 

That is, the volume of the cylinder is  times that of the sphere, so the volume of the cylinder is

.

 

Example Question #1091 : Intermediate Geometry

During a snow storm,  of snow was collected. If the snow were put in a circular lot that had a radius of , how high would the snow on the lot be?

Possible Answers:

Correct answer:

Explanation:

Since we are putting the snow on a circular base, we are dealing with a cylinder. Notice that the radius of the cylinder and the volume of the cylinder are already given to you.

Recall how to find the volume of a cylinder:

Rearrange the equation to solve for the height:

Plug in the given volume and radius:

The height is between  and  meter.

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