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The figure shown represents a piece of land that is in the shape of a quarter circle. If the land is enclosed by a fence

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The figure shown represents a piece of land that is in the shape of a quarter circle. If the land is enclosed by a fence

by BTGmoderatorDC » Sat May 09, 2020 6:30 pm

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fence.gif
The figure shown represents a piece of land that is in the shape of a quarter circle. If the land is enclosed by a fence, which of the following is closest to the length, in feet, of the fence?

(A) 278
(B) 341
(C) 357
(D) 400
(E) 441


OA C

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Re: The figure shown represents a piece of land that is in the shape of a quarter circle. If the land is enclosed by a f

by swerve » Sun May 10, 2020 6:25 am
BTGmoderatorDC wrote: ↑
Sat May 09, 2020 6:30 pm
 fence.gif

The figure shown represents a piece of land that is in the shape of a quarter circle. If the land is enclosed by a fence, which of the following is closest to the length, in feet, of the fence?

(A) 278
(B) 341
(C) 357
(D) 400
(E) 441


OA C

Source: GMAT Prep
The Central Angle of the Circle is \(90\).
The length of the Arc \(= \dfrac{90}{360} \cdot \) Circumference of the Circle
\(= 2 \cdot \pi \cdot \dfrac{100}{4} = 2 \cdot \pi \cdot 25 = 50 \cdot 3.14 = 157\)

Perimeter of the Arc \(= 100 + 100 + 157 = 357\)

Therefore, C
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