How to find the surface area of a cylinder - GRE Quantitative Reasoning
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The area of the base of a circular right cylinder is quadrupled. By what percentage is the outer face increased by this change?
The area of the base of a circular right cylinder is quadrupled. By what percentage is the outer face increased by this change?
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.)
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.)
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A cylinder has a radius of 4 and a height of 8. What is its surface area?
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!
This problem is simple if we remember the surface area formula!
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What is the surface area of a cylinder with a radius of 17 and a height of 3?
What is the surface area of a cylinder with a radius of 17 and a height of 3?
We need the formula for the surface area of a cylinder: SA = 2_πr_2 + 2_πrh_. 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
We need the formula for the surface area of a cylinder: SA = 2_πr_2 + 2_πrh_. 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
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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
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: SA of a cylinder = 2_πr_2 + 2_πrh_ = 2_π *_ 16 + 2_π_ * 4 * 2 = 48_π_
Quantity B: SA of a rectangular solid = 2_ab_ + 2_bc_ + 2_ac_ = 2 * 3 * 2 + 2 * 2 * 4 + 2 * 3 * 4 = 52
48_π_ is much larger than 52, because π is approximately 3.14.
Quantity A: SA of a cylinder = 2_πr_2 + 2_πrh_ = 2_π *_ 16 + 2_π_ * 4 * 2 = 48_π_
Quantity B: SA of a rectangular solid = 2_ab_ + 2_bc_ + 2_ac_ = 2 * 3 * 2 + 2 * 2 * 4 + 2 * 3 * 4 = 52
48_π_ is much larger than 52, because π is approximately 3.14.
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What is the surface area of a cylinder with a radius of 6 and a height of 9?
What is the surface area of a cylinder with a radius of 6 and a height of 9?
surface area of a cylinder
= 2_πr_2 + 2_πrh_
= 2_π_ * 62 + 2_π_ * 6 *9
= 180_π_
surface area of a cylinder
= 2_πr_2 + 2_πrh_
= 2_π_ * 62 + 2_π_ * 6 *9
= 180_π_
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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
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
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 = πr_2_h/3 and volume of a cylinder = πr_2_h.
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 = πr_2_h/3 and volume of a cylinder = πr_2_h.
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What is the surface area of a cylinder that has a diameter of 6 inches and is 4 inches tall?
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 
is the radius and 
is the height.
The formula for the surface area of a cylinder is
where
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A right circular cylinder of volume 
has a height of 8.
Quantity A: 10
Quantity B: The circumference of the base
A right circular cylinder of volume
Quantity A: 10
Quantity B: The circumference of the base
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 
.
The volume of any solid figure is
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