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Question Stats:
33% (00:45) correct
66% (01:08) wrong based on 3 sessions
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Square ABCD has a side length of 4. BC is the diameter of the circle. Which of the following is greater than or equal to the area of the shaded region, in square units?
Indicate all possible choices.
A. \(16 − 16\pi\)
B. \(16 − 4\pi\)
C. \(16 − 2\pi\)
D. \(16 + \pi\)
E. \(16 + 4\pi\)
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12 Apr 2024, 16:25
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Area of the square ABCD , \(4^2 = 16\)
Area of ARC BC ,
\(\frac{180}{360}*(\frac{1}{4}*pi*d^2)\) [d= diameter= 4]
\(\frac{180}{360}*(\frac{1}{4}*pi*16)\)
\(2*pi\)
So the shaded area must be equal or greater than \(16-2*pi\)
So the possible answers are C, D, E
Area of ARC BC ,
\(\frac{180}{360}*(\frac{1}{4}*pi*d^2)\) [d= diameter= 4]
\(\frac{180}{360}*(\frac{1}{4}*pi*16)\)
\(2*pi\)
So the shaded area must be equal or greater than \(16-2*pi\)
So the possible answers are C, D, E
12 Apr 2024, 16:25
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Alternative explanation
\(AB =\) side of a square \(= 4\) = diameter
Radius \(= 2\)
Area of a semicircle with radius \(2 = \frac{πr^2}{2}\)
Area \(= 2π\)
Area of a square \(= 16\)
Area of a shaded region \(= 16 - 2π\)
We need the area that can be greater than or equal to the area of the shaded region.
Answer C D E
\(AB =\) side of a square \(= 4\) = diameter
Radius \(= 2\)
Area of a semicircle with radius \(2 = \frac{πr^2}{2}\)
Area \(= 2π\)
Area of a square \(= 16\)
Area of a shaded region \(= 16 - 2π\)
We need the area that can be greater than or equal to the area of the shaded region.
Answer C D E
