If B is the center of the circle in the figure above and the area of

Question

https://gmatclub.com/forum/download/file.php?id=61857 If B is the center of the circle in the figure above and the area of the shaded region is 16π, what is the length of arc ADC? A. 4 B. 4π C. 16 D. 8π E. 16π Project PS Butler Subscribe to get Daily Email - Click Here | Subscribe via RSS - RSS 1.png

sumitkrocks · Answer

Pi*\frac{(r^2)}{4}= 16*pi 
r=8
Length of arc ADC is =  2*pi*\frac{r}{4} = 4*Pi  
(B) is the answer

rajatchopra1994 · Answer

Explanation:

Area of shaded region = 16π
1/4*πr^2 = 16π
r=8

Arc ADC length = 2πr/4 = π*8/2 = 4π

IMO-B

kantapong · Answer

Area = 1/4 (pi)r^2 = 16 pi => r^2 = 64 => r = 8
Arc length = 1/4 (2pir) = 1/2 (8pi) = 4pi (B)

asishron29181 · Answer

Given, 
Angle ABC = 90

Area of shaded region = θ/360 * pi * r^2
90/360 * pi * r^2 = 16 *pi
1/4 * pi * r^2 =16 *pi
r^2 = 64
r =8

Length of the arc = θ/360 * 2*pi*r = 1/4 * 2*pi*8 = 4 *pi

IMO B

kri1311 · Answer

It is not explicitly mentioned that Angle ABC is 90degree

Bunuel · Answer

See that little square at B? That's an indication that B is a right angle.

kri1311 · Answer

Yeah I see it. Usually in GMAT problems, I see that they mention it explicitly which wasn't the case here.

HarshaBujji · Answer

IMO B, 0.20 min.

We know that the area of this quarter circle =  1/4*\pi * r^2 ;

So we get r = 8;
Hence total perimeter is  16 \pi  , Length of ADC is  4 \pi

GmatKnightTutor · Answer

1) (90/360) times pi r^2 = 16n

2) Figure out what r is equal to algebraically

3) Plug it into the formula 2 pi r

4) Multiply the result by (90/360)

Bunuel · Answer

That is a commonly used notation in math and GMAT also uses it. For example, check the following GMAT Prep question: https://gmatclub.com/forum/in-the-figur ... 85154.html

bb · Answer

What was your logic? It shows the right angle BUT you are going to ignore it since the question stem did not mention it? 
You have to pay attention to the details on the GMAT and ask WHY rather than just sort of brush things aside and just do your thing. It is not a test of brute force but details.

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If B is the center of the circle in the figure above and the area of

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