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16 Nov 2017, 22:53
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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%
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Question Stats:
75% (01:01) correct
25%
(01:21)
wrong
based on 109
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In the figure above, a square with side of length √2 is inscribed in a circle. If the area of the circle is kπ, what is the value of k?
(A) 1/2
(B) 3/4
(C) 1
(D) 2
(E) 2√2
Attachment:
2017-11-17_0947_001.png [ 3.36 KiB | Viewed 4651 times ]
17 Nov 2017, 00:27
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The relationship between side of the square and radius of the circle is 2^1/2 to 1
So, kP=1^2*P
k=1
Answer C
So, kP=1^2*P
k=1
Answer C
17 Nov 2017, 15:44
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Bunuel
Use the square's diagonal to find diameter and radius of circle. Calculate circle's area. Set calculated area of circle equal to kπ.
The diagonal of a square with side s*: \(s\sqrt{2}\)
Given: \(s = \sqrt{2}\)
Diagonal length hence = \(\sqrt{2}*\sqrt{2}=2\)
Square's diagonal length =
length of circle's diameter, d
d = 2, and d = 2r
2 = 2r, r = 1
Area of circle = \(πr^2= (π)(1) = 1π\)
The area of the circle also = kπ
kπ = 1π
k = 1
Answer C
**OR
\(side^2 + side^2 = diagonal^2\)
\((\sqrt{2})^2 + (\sqrt{2})^2 = d^2\)
\((2 + 2) = 4 = d^2\)
\(d = 2\)
