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18 Nov 2020, 01:15
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B
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The shaded area in the figure shown consists of quarter circles. If each quarter circle has radius r, what is the area of the unshaded region in terms of r?
A. \(3r^2 - \pi r^2\)
B. \(4r^2 - \pi r^2\)
C. \(5r^2 - \pi r^2\)
D. \(6r^2 - \pi r^2\)
E. \(7r^2 - \pi r^2\)
Attachment:
2020-10-27_14-09-22.png [ 152.01 KiB | Viewed 3121 times ]
18 Nov 2020, 03:31
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IMO: B
Area of all four quarter circles = 4x(Pi r^2)/4 = Pi r^2
Area of Square = (2r)^2
Therefore, Area of unshaded region = Area of Square – Area of all four quarter circles
= 4r^2 – Pi r^2
Area of all four quarter circles = 4x(Pi r^2)/4 = Pi r^2
Area of Square = (2r)^2
Therefore, Area of unshaded region = Area of Square – Area of all four quarter circles
= 4r^2 – Pi r^2
18 Nov 2020, 09:39
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1. Area of square is side^2 and area of whole circle is (pi*(radius)^2).
2. One side of square covers two quarter circles thereby each side of square is equal to 2r where r is radius of circle
3. Area of unshaded region is Area of square - Net area of 4 quarter circles.
4. Hence area of unshaded region = (2r)^2 - ((pi*(r)^2)/4)*4 = 4r^2 - (pi*r^2)
Solution is Option B
2. One side of square covers two quarter circles thereby each side of square is equal to 2r where r is radius of circle
3. Area of unshaded region is Area of square - Net area of 4 quarter circles.
4. Hence area of unshaded region = (2r)^2 - ((pi*(r)^2)/4)*4 = 4r^2 - (pi*r^2)
Solution is Option B
