What percent of the squares area is taken up by the circle?
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A
B
C
D
E
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A. [(50 *π) / r] %
B. (25 * π) %
C. (50*π) %
D. (25 / r) %
E. (25 * r) %
OA B
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Solution:BTGmoderatorDC wrote: ↑Tue Apr 13, 2021 6:14 pmGeometry_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
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
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