### All Intermediate Geometry Resources

## Example Questions

### Example Question #60 : Cylinders

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:**

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:**

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.