2014-08-04 09:00:37

Circle A has a diameter of x. Circle B has a radius of x. What is the ratio of the area of Circle A to the area of Circle B?

(A) 1:4
(B) 1:2
(C) 1:1
(D) 2:1
(E) 4:1

The correct answer is A
Explanation: The area of a circle is calculated as πr². To find the areas of these circles, start by finding the radii. In A, if the diameter is x, then the radius is 1/2 of x, or x/2. The area, then, will be

π(x/2)² which simplifies to (x²π)/4.

The radius of B is x, so the area is πx². Thus, the ratio of A:B is (x²π)/4: x²π, which simplifies to 1/4: 1 and then finally to 1:4, the same as choice A.