For each of the three circles shown above, the diameter of the smaller

Question

Tough and Tricky questions: Geometry. https://gmatclub.com/forum/download/file.php?id=25135 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 . 2014-12-26_1941.png

littlewarthog · Answer

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.

g106 · Answer

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

qw1981 · Answer

if radius of largest circle is 8 then the medium circle's radius will be 4 and smallest circle radius will be 2.

Now area of circle = Raidus(r)*(r)*pie

hene area of shaded region= 4*4*pie- 2*2*pie= 12pie. hence answer is C

PareshGmat · Answer

Answer = C. 12π

Radius of large circle = 8, then

radius of medium circle = 4, and

radius of small circle = 2

Area of shaded region = Area of Medium circle - Area of small circle

= 16\pi - 4\pi = 12\pi

Bunuel · Answer

OFFICIAL SOLUTION:

(C) The first step is to understand the strategy. We have to find the area of the entire black circle and subtract from it the area of the smallest circle.

Since we know that the largest circle has a radius of 8, the black circle must have a radius of 4 and the smallest circle must have a radius of 2. The area of the smallest circle is equal to:
πr² = π2² = 4π.

Now, we want to find the area of the black circle:
πr² = π4² = 16π.

Finally, we subtract the smaller area from the area of the black circle to get 16π – 4π = 12π, or answer choice (C).

longhaul123 · Answer

Can someone please correct me because am not understanding as to where am i going wrong in my steps. The area of the shaded part= the total area of the largest circle - area of the smallest circle. Am i correct. if yes then , The radius of the largest circle is 8 and hence the area is 64 pi. Where am i going wrong?kindly help.

Bunuel · Answer

That's not correct. When you subtract the area of the smallest circle from the area of the largest circle you do not get the shaded region. Check the image below, you will get black region + red region, while we need only black region. Untitled.png

bumpbot · Answer

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For each of the three circles shown above, the diameter of the smaller

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For each of the three circles shown above, the diameter of the smaller

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