Such a cool question!!binaras wrote: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.
Total Surface Area Of A Cylinder = 2(Area Of Circular End) + Height(Circumference Of End)
Statement 1:
This is obviously insufficient, because it does not tell us about the heights.
Statement 2:
This is obviously insufficient, because it does not tell us about the circular dimensions.
Statements Combined:
Given that the heights of the two cylinders are equal and given that we know the ratio of the dimensions of the circular ends of the cylinders, it seems that we should be able to answer the question.
There's a trick here however. The greater the height, the more the height is a factor in the surface area of the cylinder.
Let's use some extremes.
Say the height is close to 0 and the diameters of A and B are 2 and 1 respectively.
The top of A is 4π and the area of the top of B is π. Given that the heights are negligible, the area of the sides are negligible and the ratio of the surface area of the ends is close to the ratio of the surface areas of the cylinders. So in this case the ratio is close to 4:1
Now use the same diameters, and say that the heights are 10.
Total surface area of A: 2(4Ï€) + 10(4Ï€) = 48Ï€
Total Surface Area of B: 2(Ï€) + 10(2Ï€) = 22Ï€
So the height became more of a factor and the ratio of the surface areas in this case is close to 2:1.
So we can get different ratios.
Insufficient.
The correct answer is E.
