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Each of the three shaded regions above is a semicircle. If AB = 4, CD

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Carcass
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Each of the three shaded regions above is a semicircle. If AB = 4, CD [#permalink] New post   07 Apr 2022, 05:44
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Each of the three shaded regions above is a semicircle. If AB = 4, CD = 2BC, and BC = 2AB, then the area of the entire shaded figure is

A. 28π
B. 42π
C. 84π
D. 96π
E. 168π
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Re: Each of the three shaded regions above is a semicircle. If AB = 4, CD [#permalink] New post   07 Apr 2022, 05:50
Carcass wrote:
Image
Each of the three shaded regions above is a semicircle. If AB = 4, CD = 2BC, and BC = 2AB, then the area of the entire shaded figure is

A. 28π
B. 42π
C. 84π
D. 96π
E. 168π

From the given information, we get:
Image

The diameter of the smallest semicircle is 4, which means its radius = 2
The diameter of the middle semicircle is 8, which means its radius = 4
The diameter of the largest semicircle is 16, which means its radius = 8

Area of semicircle \(= \frac{\pi r^2}{2}\)
So, the area of the smallest semicircle \(= \frac{\pi (2^2)}{2} = 2 \pi\)
The area of the middle semicircle \(= \frac{\pi (4^2)}{2} = 8 \pi\)
The area of the largest smallest semicircle \(= \frac{\pi (8^2)}{2} = 32 \pi\)

So, the TOTAL shaded area \(= 2 \pi + 8 \pi + 32 \pi = 42 \pi \)

Answer: B
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Re: Each of the three shaded regions above is a semicircle. If AB = 4, CD [#permalink] New post   28 Apr 2024, 16:49
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Each of the three shaded regions above is a semicircle. If AB = 4, CD [#permalink]
28 Apr 2024, 16:49
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