### All ISEE Upper Level Quantitative Resources

## Example Questions

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

What is the volume of a cylinder with a radius of 6 meters and a height of 11 meters? Use 3.14 for .

Note: The formula for the volume of a cylinder is:

**Possible Answers:**

**Correct answer:**

To calculate the volume, you must plug into the formula given in the problem. When you plug in, it should look like this: . Multiply all of these out and you get . The units are cubed because volume is always cubed.

### Example Question #1 : Cylinders

The volume of a cylinder whose height is twice the diameter of its base is one cubic yard. Give its radius in inches.

**Possible Answers:**

**Correct answer:**

The volume of a cylinder with base radius and height is

The diameter of this circle is ; its height is twice this, or . Therefore, the formula becomes

Set this volume equal to one and solve for :

This is the radius in yards; multiply by 36 to get the radius in inches.

### Example Question #1 : Cylinders

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

**Possible Answers:**

**Correct answer:**

Recall that the equation of for the volume of a cylinder is:

For our values this is:

Solve for :

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

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

**Possible Answers:**

**Correct answer:**

This is a rather direct question. Recall that the equation of for the volume of a cylinder is:

For our values this is:

This is the volume of the cylinder.

### Example Question #1 : Cylinders

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

**Possible Answers:**

**Correct answer:**

This is a rather direct question. Recall that the equation of for the volume of a cylinder is:

For our values this is:

This is the volume of the cylinder.

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

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

**Possible Answers:**

**Correct answer:**

Recall that the equation of for the volume of a cylinder is:

For our values this is:

Solve for :

Using a calculator to calculate , you will see that