sandipgumtya wrote:"ABC and CDE are two identical semi-circles of radius 2 units. B and D are the mid points of the arc ABC and CDE respectively. What is the area of the shaded region? "
(A)4pi - 1
(B)3pi - 1
(C)2pi - 4
(D)(3pi - 1)/2
(E)2pi-2
Let's apply some ESTIMATION.
We can do so because, unless specified otherwise, the diagrams in Problem Solving questions
are drawn to scale.
If we combine the two semi-circles, we get a complete circle with radius 2.
Area of circle = (pi)(r²) = (pi)(2²) = 4(pi) ≈ 4(3) ≈
12
So, the total area of the two semi-circles is APPROXIMATELY
12
Now, let's ESTIMATE the portion of the semi-circles that's shaded.
Hmmm, looks like ABOUT
1/5 (or perhaps 1/6) is shaded.
1/5 of
12 = 12/5 = 2 2/5 =
2.SOMETHING
Let's check the answer choices to see if any of them are APPROXIMATELY
2.SOMETHING
(A)4pi - 1 ≈ 4(3) - 1 ≈ 11 not even close to
2.SOMETHING
(B)3pi - 1 ≈ 3(3) - 1 ≈ 8 not even close to
2.SOMETHING
(C)2pi - 4 ≈ 2(3) - 4 ≈ 2 looks good. KEEP
(D)(3pi - 1)/2 ≈ [3(3) - 1]/2 ≈ 4 not even close to
2.SOMETHING
(E)2pi-2 ≈ 2(3)-2 ≈ 4 not even close to
2.SOMETHING
Answer:
C
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
