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Wed Mar 03, 2021 10:54 am

GMAT Prep

An artist is painting a white circular region on the top surface of a square blue tile that measures 8 inches on a side. If the circle is inscribed in the square, what fraction of the top surface of the tile will be blue?

A. \(1/4\)
B. \(1/2\)
C. \(\pi/4\)
D. \((4-\pi)/\pi\)
E. \((4-\pi)/4\)

OA E

Solution:

The diameter of the inscribed circular region is the same as the side of the square tile; thus, it’s 8 inches. Therefore, the area of the circular region is π x (8/2)^2 = 16π sq. inches. Since the area of the square is 8^6 = 64 sq. inches, the area of the square tile that is still blue is 64 - 16π sq. inches. Therefore, the fraction of the square tile that is still blue is (64 - 16π) / 64 = (4 - π) / 4.

Answer: E