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10 Jan 2016, 08:58
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B
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:
76% (00:56) correct
24%
(00:56)
wrong
based on 66
sessions
History
Date
Time
Result
Not Attempted Yet
A square, with perimeter 16, is inscribed in a circle. What is the area of the circle?
A. 4π
B. 8π
C. 12π
D. 16π
E. 32π
A. 4π
B. 8π
C. 12π
D. 16π
E. 32π
Praveengeol
Joined: 02 Jun 2015
Last visit: 14 Nov 2017
Posts: 55
Given Kudos: 27
Location: United States
Concentration: Strategy, Human Resources
Schools: Schulich Sept"18 (A)
WE:Engineering (Manufacturing)
10 Jan 2016, 09:15
Kudos
Bookmarks
Bunuel
Area of circuscribed circle = pi/2*area of square
Area of square = (16/4)^2 = 4^2= 16
Area of circle = pi/2*16=8pi
Answer B
12 Sep 2019, 08:26
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Bunuel
Since the Square is inscribed in a circle the vertext of the square touches the circle , further opposite faces (diagonals) touches the Circumferenceof the Circle and forms the Diameter (From which we can obtain the radius and find the area of the circle)
\(4a = 16\)
So, \(a = 4\)
Diagonal of the square is \(4\sqrt{2}\) So, radius of the circle is \(4\sqrt{2}\)
Thus, Area of the circle will be \(π*2\sqrt{2}*2\sqrt{2}=8π\) , Answer must be (B)
12 Sep 2019, 08:36
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Bunuel
Side of square = 16/4 = 4
Diagonal of the square = \(4\sqrt{2}\) = 2r
r = \(2\sqrt{2}\)
Area of the circle = \(\pi * (2\sqrt{2})^2 = \pi *8\)
IMO B
