What percent of the squares area is taken up by the circle?

[B BTGmoderatorDC]

Geometry_Q1_Image.jpg

What percent of the square’s area is taken up by the circle?

A. [(50 *π) / r] %

B. (25 * π) %

C. (50*π) %

D. (25 / r) %

E. (25 * r) %


OA B

Source: Veritas Prep

[Scott@TargetTestPrep]

Geometry_Q1_Image.jpg

What percent of the square’s area is taken up by the circle?

A. [(50 *π) / r] %

B. (25 * π) %

C. (50*π) %

D. (25 / r) %

E. (25 * r) %


OA B

Solution:

The area of the circle is πr^2 and the area of the square is (2r)^2 = 4r^2. Therefore, the area circle is πr^2 / (4r^2) x 100 = π/4 x 100 = 25π percent of the area of the square.

Alternate Solution:

The percent of the square’s area taken up by the circle is independent of the circle’s radius; thus we can immediately eliminate choices A, D, and E. It is impossible for an inscribed circle to take up more than 100% of the square; thus, we eliminate answer choice C as well (notice that 50 * π is greater than 100). The only remaining answer choice is B.

Answer: B