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Cylinder A, which has a radius of x and a height of y, has a greater surface area than does Cylinder B, which has a radius of y and a height of x. How much greater is the surface area of Cylinder A than that of Cylinder of B?

Hi! Well your question is a little bit ambiguous... However, as you mentioned, it is a good question.

So let’s try to get areas of Cylinder A and B.

First of all a Cylinder has two circles(bottom and top) and a rectangle(side) so the area of Cylinder A is 2*pi*x^2 + 2*pi*x*y.

Similarly the area of Cynlinder B is 2*pi*y^2 + 2*pi*x*y.

Since Cylinder A has a greater surface area than does Cylinder B, x > y.

So the difference of area is 2*pi*x^2 + 2*pi*x*y -(2*pi*y^2 + 2*pi*x*y) = 2*pi(x^2 –y^2)

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