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02 Feb 2016, 01:57
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E
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Difficulty:
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In the figure above, the centers of four equal circles lie along the diameter of the large circle. If the circumference of the large circle is 64π, what is the area of the shaded region?
A. 16π
B. 32π
C. 64π
D. 128π
E. 256π
Attachment:
2016-01-31_1804.png [ 4.24 KiB | Viewed 3242 times ]
Editing my solution:
2*pi*r = 64*pi
r = 32
d1 + d2 + d3 + d4 = 2*32
Since d1 = d2 = d3 = d4; 4d1 = 64
d1 = 16
d1 = 2r1
r1 = 8
Area of one shaded circle = pi*(8^2) = 64pi
Area of four shaded circles = 4*64pi = 256pi
Answer: E
2*pi*r = 64*pi
r = 32
d1 + d2 + d3 + d4 = 2*32
Since d1 = d2 = d3 = d4; 4d1 = 64
d1 = 16
d1 = 2r1
r1 = 8
Area of one shaded circle = pi*(8^2) = 64pi
Area of four shaded circles = 4*64pi = 256pi
Answer: E
nklotz
Joined: 10 Jul 2014
Last visit: 12 Apr 2016
Posts: 3
Given Kudos: 19
Concentration: Finance, Strategy
Schools: Kellogg '18 Ross '18 Stern '18 Tuck '18 Booth EMBA'18
03 Feb 2016, 09:43
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C = pi * D
D of large circle = 64
D of each black circle = 64/4 = 16
r of each black circle = 8
A = pi * r^2
A of each black circle = pi * 8^2 = 64 * pi
Total A of black circles = 4 * 64 * pi = 256 * pi
Answer = E
D of large circle = 64
D of each black circle = 64/4 = 16
r of each black circle = 8
A = pi * r^2
A of each black circle = pi * 8^2 = 64 * pi
Total A of black circles = 4 * 64 * pi = 256 * pi
Answer = E
