GRE Math : How to find the surface area of a cylinder
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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?
400%
100%
250%
200%
300%
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 #2 : Solid Geometry
What is the surface area of a cylinder with a radius of 17 and a height of 3?
2137
2205
2000
3107
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 #2 : How To Find The Surface Area Of A Cylinder
What is the surface area of a cylinder with a radius of 6 and a height of 9?
64π
225π
180π
108π
96π
180π
surface area of a cylinder
= 2πr2 + 2πrh
= 2π * 62 + 2π * 6 *9
= 180π
Example Question #3 : 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.
Quantity A is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
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 #1 : Cylinders
A right circular cylinder of volume 
Quantity A: 10
Quantity B: The circumference of the base
Quantity A is greater
Quantity B is greater
The two quantities are equal
The relationship cannot be determined from the information provided.
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 #1 : Cylinders
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 #7 : 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
Quantity A is greater.
Quantity B is greater.
The relationship cannot be determined from the information given.
The two quantities are equal.
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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