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Tough and Tricky questions: Geometry.
For each of the three circles shown above, the diameter of the smaller circle is equal to the radius of the larger. If the radius of the largest circle is equal to 8 inches, what is the area of the shaded region in square inches?
A. 3π
B. 6π
C. 12π
D. 15π
E. 18π
Kudos for a correct solution.
Attachment:
2014-12-26_1941.png [ 3.5 KiB | Viewed 10671 times ]
26 Dec 2014, 09:27
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Quote:
For each of the three circles shown above, the diameter of the smaller circle is equal to the radius of the larger. If the radius of the largest circle is equal to 8 inches, what is the area of the shaded region in square inches?
A. 3π
B. 6π
C. 12π
D. 15π
E. 18π
A. 3π
B. 6π
C. 12π
D. 15π
E. 18π
Starting from the largest circle, we first calculate the radii of the smaller circles:
We are told that the largest radius is 8 inches: \(r_{3}=8\). From this follows \(r_{2}=4\) and \(r_13}=2\). (\(r_{1}\) is the radius of the smallest circle and \(r_{2}\) the radius of the middle circle.
The shaded area is then \(\pi * r_{2}^2 - \pi * r_{1}^2 = \pi * (r_{2}^2 - r_{1}^2) = \pi * 12 = 12\pi\).
Answer C.
26 Dec 2014, 17:49
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Bunuel
Tough and Tricky questions: Geometry.
For each of the three circles shown above, the diameter of the smaller circle is equal to the radius of the larger. If the radius of the largest circle is equal to 8 inches, what is the area of the shaded region in square inches?
A. 3π
B. 6π
C. 12π
D. 15π
E. 18π
Kudos for a correct solution.
Attachment:
2014-12-26_1941.png
Say circles as A B C with Smallest is A and Largest is C
Radius of C = 8; B=4;C=2
Area of Shaded region = Area of B-Area of A
= 16 π - 4 π
= 12 π
Ans C
