# GRE Math : How to find the surface area of a cylinder

## Example Questions

### Example Question #1 : Solid Geometry

The area of the base of a circular right cylinder is quadrupled. By what percentage is the outer face increased by this change?

100%

200%

400%

250%

300%

100%

Explanation:

The base of the original cylinder would have been πr2, and the outer face would have been 2πrh, where h is the height of the cylinder.

Let's represent the original area with A, the original radius with r, and the new radius with R: therefore, we know πR2 = 4A, or πR24πr2. Solving for R, we get R = 2r; therefore, the new outer face of the cylinder will have an area of 2πRh or 2π2rh or 4πrh, which is double the original face area; thus the percentage of increase is 100%. (Don't be tricked into thinking it is 200%. That is not the percentage of increase.)

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

What is the surface area of a cylinder with a radius of 17 and a height of 3?

2137

2205

2000

3107

1984

2137

Explanation:

We need the formula for the surface area of a cylinder: SA = 2πr2 + 2πrh. This formula has π in it, but the answer choices don't. This means we must approximate π. None of the answers are too close to each other so we could really even use 3 here, but it is safest to use 3.14 as an approximate value of π.

Then SA = 2 * 3.14 * 172 + 2 * 3.14 * 17 * 3 ≈ 2137

### Example Question #2 : Solid Geometry

What is the surface area of a cylinder with a radius of 6 and a height of 9?

225π

180π

108π

96π

64π

180π

Explanation:

surface area of a cylinder

= 2πr2 + 2πrh

= 2π * 62 + 2π * 6 *9

= 180π

### Example Question #2 : Solid Geometry

Quantitative Comparison

Quantity A: The volume of a cylinder with a radius of 3 and a height of 4

Quantity B: 3 times the volume of a cone with a radius of 3 and a height of 4

Quantity B is greater.

The relationship cannot be determined from the information given.

The two quantities are equal.

Quantity A is greater.

The two quantities are equal.

Explanation:

There is no need to do the actual computations here to find the two volumes. The volume of a cone is exactly 1/3 the volume of a cylinder with the same height and radius. That means the two quantities are equal. The formulas show this relationship as well: volume of a cone = πr2h/3 and volume of a cylinder = πr2h

### Example Question #2 : Solid Geometry

A right circular cylinder of volume  has a height of 8.

Quantity A: 10

Quantity B: The circumference of the base

Quantity B is greater

The relationship cannot be determined from the information provided.

The two quantities are equal

Quantity A is greater

Quantity B is greater

Explanation:

The volume of any solid figure is . In this case, the volume of the cylinder is  and its height is , which means that the area of its base must be . Working backwards, you can figure out that the radius of a circle of area  is . The circumference of a circle with a radius of  is , which is greater than .

### Example Question #3 : Solid Geometry

What is the surface area of a cylinder that has a diameter of 6 inches and is 4 inches tall?

Explanation:

The formula for the surface area of a cylinder is ,

where  is the radius and is the height.

### Example Question #4 : Solid Geometry

A cylinder has a radius of 4 and a height of 8.  What is its surface area?

Explanation:

This problem is simple if we remember the surface area formula!

### Example Question #5 : Solid Geometry

Quantitative Comparison

Quantity A: Surface area of a cylinder that is 2 feet high and has a radius of 4 feet

Quantity B: Surface area of a box that is 3 feet wide, 2 feet high, and 4 feet long

The relationship cannot be determined from the information given.

Quantity A is greater.

Quantity B is greater.

The two quantities are equal.

Quantity A is greater.

Explanation:

Quantity A: SA of a cylinder = 2πr2 + 2πrh = 2π * 16 + 2π * 4 * 2 = 48π

Quantity B: SA of a rectangular solid = 2ab + 2bc + 2ac = 2 * 3 * 2 + 2 * 2 * 4 + 2 * 3 * 4 = 52

48π is much larger than 52, because π is approximately 3.14.