# GMAT Math : Cylinders

## Example Questions

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### Example Question #1 : Calculating The Surface Area Of A Cylinder

What is the surface area of a cylinder with a radius of 7 and a height of 3?

Explanation:

All we really need here is to remember the formula for the surface area of a cylinder.

### Example Question #501 : Geometry

The height of a cylinder is twice the circumference of its base. The radius of the base is 9 inches. What is the surface area of the cylinder?

Explanation:

The radius of the base is 9 inches, so its circumference is  times this, or  inches. The height is twice this, or  inches.

Substitute  in the formula for the surface area of the cylinder:

square inches

### Example Question #1 : Cylinders

Calculate the surface area of the following cylinder.

(Not drawn to scale.)

Explanation:

The equation for the surface area of a cylinder is:

we plug in our values:  to find the surface area

### Example Question #1 : Cylinders

Calculate the surface area of the following cylinder.

(Not drawn to scale.)

Explanation:

The equation for the surface area of a cylinder is

We plug in our values  into the equation to find our answer.

Note: we were given the diameter of the cylinder (10), in order to find the radius we had to divide the diameter by two.

### Example Question #1 : Calculating The Surface Area Of A Cylinder

A cylinder has a height of 9 and a radius of 4. What is the total surface area of the cylinder?

Explanation:

We are given the height and the radius of the cylinder, which is all we need to calculate its surface area. The total surface area will be the area of the two circles on the bottom and top of the cylinder, added to the surface area of the shaft. If we imagine unfolding the shaft of the cylinder, we can see we will have a rectangle whose height is the same as that of the cylinder and whose width is the circumference of the cylinder. This means our formula for the total surface area of the cylinder will be the following:

### Example Question #501 : Geometry

Grant is making a canister out of sheet metal. The canister will be a right cylinder with a height of  mm. The base of the cylinder will have a radius of  mm. If the canister will have an open top, how many square millimeters of metal does Grant need?

Explanation:

This question is looking for the surface area of a cylinder with only 1 base. Our surface area of a cylinder is given by:

However, because we only need 1 base, we can change it to:

We know our radius and height, so simply plug them in and simplify.

### Example Question #7 : Calculating The Surface Area Of A Cylinder

Find the surface area of a cylinder whose height is  and radius is .

Explanation:

To find the surface area of a cylinder, you must use the following equation.

Thus,

### Example Question #1 : Cylinders

A right circular cylinder has bases of radius ; its height is . Give its surface area.

Explanation:

The surface area of a cylinder can be calculated from its radius and height as follows:

Setting  and :

or

### Example Question #1 : Calculating The Volume Of A Cylinder

What is the volume of a cone with a radius of 6 and a height of 7?

Explanation:

The only tricky part here is remembering the formula for the volume of a cone. If you don't remember the formula for the volume of a cone, you can derive it from the volume of a cylinder. The volume of a cone is simply 1/3 the volume of the cylinder. Then,

### Example Question #1 : Calculating The Volume Of A Cylinder

What is the volume of a sphere with a radius of 9?