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The circle is inscribed in a square that has an area of 50. What is the area of the circle?

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by BTGmoderatorLU » Sat Oct 31, 2020 6:26 am

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Source: Manhattan Prep
Capture (3).JPG
In the figure above, the circle is inscribed in a square that has an area of 50. What is the area of the circle?

A. \(\dfrac{25\pi}{4}\)

B. \(\dfrac{25\pi}{2}\)

C. \(25\pi\)

D. \(50\pi\)

E. \(\dfrac{625\pi}{16}\)

The OA is B
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Re: The circle is inscribed in a square that has an area of 50. What is the area of the circle?

by jhavyom » Sun Nov 01, 2020 12:14 am
BTGmoderatorLU wrote: ↑
Sat Oct 31, 2020 6:26 am
 Source: Manhattan Prep

Capture (3).JPG

In the figure above, the circle is inscribed in a square that has an area of 50. What is the area of the circle?

A. \(\dfrac{25\pi}{4}\)

B. \(\dfrac{25\pi}{2}\)

C. \(25\pi\)

D. \(50\pi\)

E. \(\dfrac{625\pi}{16}\)

Let the side of the square be d.
Also, the diameter of the circle is d.

Area of square = \(^{d^2} = 50 \)

Area of circle =\( \dfrac{\pi }{4}*^{d^2}\)
=\(\dfrac{\pi}{4}\) *50
= \(\dfrac{25\pi}{2}\)
Option B is the answer.
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