GRE Math : How to find the surface area of a cylinder
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Example Questions
Example Question #1 : How To Find The Surface Area Of A Cylinder
The area of the base of a circular right cylinder is quadrupled. By what percentage is the outer face increased by this change?
200%
400%
100%
300%
250%
100%
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 πR2 = 4πr2. 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 : Solid Geometry
What is the surface area of a cylinder with a radius of 17 and a height of 3?
2205
3107
2000
2137
1984
2137
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 #1501 : Gre Quantitative Reasoning
What is the surface area of a cylinder with a radius of 6 and a height of 9?
96π
64π
180π
108π
225π
180π
surface area of a cylinder
= 2πr2 + 2πrh
= 2π * 62 + 2π * 6 *9
= 180π
Example Question #1 : Cylinders
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 two quantities are equal.
The relationship cannot be determined from the information given.
Quantity A is greater.
The two quantities are equal.
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 #4 : Cylinders
A right circular cylinder of volume 
Quantity A: 10
Quantity B: The circumference of the base
The relationship cannot be determined from the information provided.
Quantity B is greater
The two quantities are equal
Quantity A is greater
Quantity B is greater
The volume of any solid figure is 
Example Question #1 : Solid Geometry
What is the surface area of a cylinder that has a diameter of 6 inches and is 4 inches tall?
The formula for the surface area of a cylinder is 
where 
Example Question #2 : Solid Geometry
A cylinder has a radius of 4 and a height of 8. What is its surface area?
This problem is simple if we remember the surface area formula!
Example Question #3 : Cylinders
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 two quantities are equal.
The relationship cannot be determined from the information given.
Quantity B is greater.
Quantity A is greater.
Quantity A is greater.
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.
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