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10 Mar 2015, 06:07
Kudos
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B
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Difficulty:
5%
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Question Stats:
88% (01:22) correct
12%
(01:51)
wrong
based on 244
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In the figure above, AC = BC = 8, angle C = 90°, and the circular arc has its center at point C. Find the area of the shaded region.
A. \(8\pi-32\)
B. \(16\pi-32\)
C. \(16\pi-64\)
D. \(32\pi-32\)
E. \(32\pi-64\)
Kudos for a correct solution.
Attachment:
gm-tuaaof_img1.png [ 5.79 KiB | Viewed 7852 times ]
27 Feb 2018, 10:24
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Bunuel
Area of shaded region = (area of sector) - (area of triangle)
Area of circle = π(radius)²
Area of triangle = (base)(height)/2
The sector ABC is 1/4 of a circle of radius 8
So, area of sector = (1/4)(π)(8²)
= 16π
area of triangle = (8)(8)/2
= 32
So, area of shaded region = (16π) - (32)
Answer: B
Cheers,
Brent
General Discussion
10 Mar 2015, 06:33
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Hi
Area of sector = (90/360)*pi(8^2) = 16pi
Area of triangle = (1/2)*8*8 = 32
Area of shaded region = area of sector - area of triangle = 16pi-32
Area of sector = (90/360)*pi(8^2) = 16pi
Area of triangle = (1/2)*8*8 = 32
Area of shaded region = area of sector - area of triangle = 16pi-32
