Problem Solving

Hi swerve,

We're told that the surface of a cylinder of radius R and height H is painted: the two bases of the cylinder are painted red, and the side of the cylinder is painted green and the red area is equal to the green area. We're asked which of the following must be true. To answer this question, you first need the area formulas involved.

The 'top' and 'bottom' of the cylinder are circles, so each of those two areas is (pi)(R^2). The total of those 2 areas is: (2)(pi)(R^2).
The 'side' of the cylinder is the CIRCUMFERENCE of the circle multiplied by the height. That area is (2)(pi)(R)(H).

We're told that the two areas are EQUAL to one another, so....
(2)(pi)(R^2) = (2)(pi)(R)(H)

You can 'cancel out' the 2s and the pis....
(R^2) = (R)(H)
R = H

Final Answer: A

GMAT assassins aren't born, they're made,
Rich