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18 Jun 2021, 01:30
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B
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In the figure shown, a circle with center O is inscribed in a square. If the area of the circle is 16π, what is the total area of all of the shaded regions?
A. 24
B. 32
C. 48
D. 56
E. 64
Attachment:
1.png [ 3.19 KiB | Viewed 3428 times ]
18 Jun 2021, 02:53
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From the symmetry, we can say the area of the shaded area is half of the area of the square
Area of inscribed circle = \(16* pi\) = Pi * \(r^2\) (r =radius of the circle )
r= 4
Side of the square = a = \(2*r\) = 8
Area of the square = \(a^2\) = 64
Area of the shaded region =\( \frac{64}{2} \)= 32
B is the correct answer IMO
Area of inscribed circle = \(16* pi\) = Pi * \(r^2\) (r =radius of the circle )
r= 4
Side of the square = a = \(2*r\) = 8
Area of the square = \(a^2\) = 64
Area of the shaded region =\( \frac{64}{2} \)= 32
B is the correct answer IMO
Bunuel
asishron29181
Joined: 04 May 2020
Last visit: 04 Nov 2022
Posts: 185
Given Kudos: 68
Location: India
Schools: Great Lakes (I)
GMAT 1: 610 Q47 V27
WE:Programming (Computer Software)
18 Jun 2021, 03:18
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Given area of circle = π * r^2 = 16 π
r = 4
Diameter = 8
Area of two shaded portions inside the circle = 16 π /2 = 8 π
Area of square = 8^2 = 64
Area of square - Area of circle = 64 - 16 π
Area of two shaded portions between the square and circle = 64 - 16 π / 2
32 - 8 π
Combined area of shaded regions = 32 - 8 π + 8 π = 32
IMO B
r = 4
Diameter = 8
Area of two shaded portions inside the circle = 16 π /2 = 8 π
Area of square = 8^2 = 64
Area of square - Area of circle = 64 - 16 π
Area of two shaded portions between the square and circle = 64 - 16 π / 2
32 - 8 π
Combined area of shaded regions = 32 - 8 π + 8 π = 32
IMO B
