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28 Jun 2020, 10:43
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B
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Difficulty:
15%
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Question Stats:
84% (01:06) correct
16%
(00:42)
wrong
based on 44
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A circle is circumscribed over a square of perimeter 8. What is the area of the circle?
A. \(\sqrt{2}\)*pi
B. 2*pi
C. 2*\(\sqrt{2}\)*pi
D. 4*pi
E. 6*pi
A. \(\sqrt{2}\)*pi
B. 2*pi
C. 2*\(\sqrt{2}\)*pi
D. 4*pi
E. 6*pi
28 Jun 2020, 10:48
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kapil1
The side of the square = 8/4 = 2.
The diagonal of the square is \(\sqrt{2^2+2^2}=2\sqrt{2}\).
The diagonal of the square = the diameter of the circle. Therefore, the radius = \(\sqrt{2}\) (half the diameter ).
The area = \(\pi r^2=2\pi\)
Answer: B.
28 Jun 2020, 12:07
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B.
When Circle circumscribe the square ==> Diagonal of square will become the diameter of the circle.
Perimeter of Square = 4 * Side = 8
=> Side =2
Diagonal of square = \(\sqrt{2}\) * Side
=> Diagonal =2\(\sqrt{2}\)
=>Diameter of Circle= 2\(\sqrt{2}\)
or Radius of circle = \(\sqrt{2}\)
Area of Circle = π (\(radius^2\)) = 2π
When Circle circumscribe the square ==> Diagonal of square will become the diameter of the circle.
Perimeter of Square = 4 * Side = 8
=> Side =2
Diagonal of square = \(\sqrt{2}\) * Side
=> Diagonal =2\(\sqrt{2}\)
=>Diameter of Circle= 2\(\sqrt{2}\)
or Radius of circle = \(\sqrt{2}\)
Area of Circle = π (\(radius^2\)) = 2π
