The surface area of cylinder A is how many times the surface area of

Question

The surface area of cylinder A is how many times the surface area of cylinder B?

(1) The diameter of A is twice the diameter of B.
(2) The height of A is equal to the height of B.

TestPrepUnlimited · Answer

The surface area is directly proportional to the height and the radius of a cylinder, so we need the ratio of heights and the ratio of radii to find the ratio of surface areas. Then we need to combine statements to find the ratio. Sufficient when combined.

Ans: C

stne · Answer

Clearly each statement by itself is INSUFF.

1+2

Let larger cylinder D be  20   hence radius  10  
Smaller cylinder D be  10  hence radius is  5

Total surface area :  2(\pi r^2) + 2\pi r *h

Cylinder A :  2\pi*(10)^2 + 2\pi*10 *h = 2\pi

Cylinder B = 2\pi*(5)^2 + 2\pi*5*h = 2\pi

\frac {A}{B} = \frac {2\pi (100 +10h)}{2\pi (25 +5h)}

= \frac {2 (10+h)}{ 5+ h}

Since we don't know  h  we still cannot find the ratio.

Ans= E

Hope it's clear.

Harshjha001 · Answer

It's a very vague question IMO .
Its never mentioned if its an open cylinder or closed cylinder or closed cylinder with one side open etc.

IanStewart · Answer

You can answer this question conceptually, if you know how areas change when you scale various dimensions. If you double every length in a shape (or double the radius of a circle), the shape's area will increase by a factor of 4. If, on the other hand, you only double one length in a shape (e.g. if you double the length of a rectangle, or the base of a triangle), area will also simply double.

The surface area of a cylinder can be divided into two parts: we have the two circular ends, and then the 'wrap-around' part between those ends, which is, if we unwrap it, just a rectangle. Using both Statements, when we double the radius of cylinder B and leave the height alone to make cylinder A, we're doubling the radius of the circles, and the area of the circular ends will quadruple. But we're only doubling the length (not the height) of the wrap-around rectangle, so its area will only double. So one part of A's surface area is 4 times that of B, while the other part is only 2 times that of B, and all we know is that the surface area of A is somewhere between 2 and 4 times the surface area of B. It matters if the height is small or large, relative to the radius. If the height of both cylinders is almost zero, then the surface area of A will be almost 4 times that of B, because then the circles are almost all that matter, but if the height is large compared to the radius, the ratio will be close to 2 to 1. It's exactly like the question: If Asha has 4 times as many red marbles as Sam, and 2 times as many blue marbles as Sam, and they only have red and blue marbles, then the number of marbles Asha has is how many times the number Sam has? All we can say is that the answer is between 2 and 4, but we'd need more information about the balance of red and blue marbles to say any more than that.

Naturally one can do the problem algebraically as well. If B has a radius of r and a height of h, its surface area is 2πr^2 + 2πrh = 2πr(r + h). Then A has a radius of 2r, and a height of h, and its surface area is 2π(2r)^2 + 2π(2r)h = 8πr^2 + 4πrh = 4πr^2 + 4πr^2 + 4πrh = 4πr^2 + 4πr(r + h). The ratio of A's surface area to B's is then:

(4πr^2 + 4πr(r + h)) / 2πr(r + h) = (2r + 2(r + h))/(r + h) =   + 2

from which we see that the ratio is automatically greater than 2 (since we're adding 2 to a positive number) and is automatically less than 4 (since r/(r+h) must be less than 1 -- notice when h is close to zero, the answer is very close to 4, as expected), but we can't find an exact value, and the answer is E.

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