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05 Jul 2021, 04:45
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
79% (01:18) correct
21%
(01:37)
wrong
based on 126
sessions
History
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If the square is inscribed in the circle above, and the area of the square is 50, what is the area of the circle?
A. \(\frac{25\pi}{4}\)
B. \(\frac{25\pi}{2}\)
C. \(25\pi\)
D. \(50\pi\)
E. \(\frac{625\pi}{16}\)
Attachment:
2021-06-18_00-27-12.png [ 11.42 KiB | Viewed 2989 times ]
05 Jul 2021, 07:55
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Bunuel
\(50 = \frac{d^2}{2}\)
So, \(d = \sqrt{100}\)
Thus, \(d = 10\) & \(r = 5\)
Now area of circle will be \(π*5*5 = 25π\), Answer must be (C)
05 Jul 2021, 10:52
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Solution:
Area of square is given \(= 50.\)
squarecircle.png [ 10.26 KiB | Viewed 2679 times ]
\(⇒ a^2 = 50\)
\(⇒ a = \sqrt{50}\)
we know diagonal of square \(= a\sqrt{2} = \sqrt{50\times 2} = \sqrt{100} = 10\)
We can see that diagonal of square \(= 2r\) (where \(r\) is the radius of the circle)
So, \(2r = 10\)
\(⇒ r = \frac{10}{2} = 5\)
Area of the circle \(= \pi r^2 = 25\pi\)
Hence the right answer is Option C.
Area of square is given \(= 50.\)
Attachment:
squarecircle.png [ 10.26 KiB | Viewed 2679 times ]
\(⇒ a^2 = 50\)
\(⇒ a = \sqrt{50}\)
we know diagonal of square \(= a\sqrt{2} = \sqrt{50\times 2} = \sqrt{100} = 10\)
We can see that diagonal of square \(= 2r\) (where \(r\) is the radius of the circle)
So, \(2r = 10\)
\(⇒ r = \frac{10}{2} = 5\)
Area of the circle \(= \pi r^2 = 25\pi\)
Hence the right answer is Option C.
