Two circular signs are to be painted. If the radius of the larger sign is five times that of the smaller sign, how many times more paint is needed to paint the larger sign? (We can assume that a given amount of paint covers the same area on both signs.)
Choose the correct choice:
A) 5 B) 15 C) 25 D) 35 E) 45
Let R be the radius of the smaller sign.   The area A of the smaller sign is A = piR^2.   The area of the larger sign is pi(5R)^2=25piR^2=25A.   Since the area is 25 times larger, we need 25 times more paint for the larger sign.   The answer is 25.
<result>C</result>
Two circular signs are to be painted. If the radius of the larger sign is five times that of the smaller sign, how many times more paint is needed to paint the larger sign? (We can assume that a given amount of paint covers the same area on both signs.)