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The figure above shows a circle inscribed in a square which
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21 Feb 2020, 11:47
21 Feb 2020, 11:47
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The figure above shows a circle inscribed in a square which is in turn inscribed within a larger circle. What is the ratio of the area of the larger circle to that of the smaller circle?
A. \(\sqrt{2}\)
B. \(\frac{\pi}{2}\)
C. \(\frac{\pi^2}{4 \sqrt{2 }}\)
D. \(2\)
E. \(\frac{\pi}{\sqrt{2}}\)
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GRE 1: Q167 V152
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Re: The figure above shows a circle inscribed in a square which
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23 Feb 2020, 02:49
23 Feb 2020, 02:49
1
Lets assume that one side of square can be referred by 's'.
In the figure, it can be seen that a side of the square is equal to the diameter of the smaller circle.
Diameter of small circle = s
Radius of small circle = s / 2
The diagonal of the square is equal to the diameter of big circle
Diameter of big circle = s * (2)^0.5
Radius of big circle = (s * 2^0.5)/2
Area of small circle = pi * radius^2 = pi * (s/2)^2
Area of small circle = pi * (s^2)/4
Area of big circle = pi * radius^2 = pi * [(s * 2^0.5)/2]^2 = pi * [((s^2) * 2)/4]
Area of big circle = pi * [(s^2)/2]
Ratio of Area of big circle to Area of small circle = [pi * (s^2)/2] / [pi * (s^2)/4]
After cancelling out pi and s^2, we get:
Ratio of Area of big circle to Area of small circle = 4 / 2 = 2
Therefore, the answer is D) 2.
In the figure, it can be seen that a side of the square is equal to the diameter of the smaller circle.
Diameter of small circle = s
Radius of small circle = s / 2
The diagonal of the square is equal to the diameter of big circle
Diameter of big circle = s * (2)^0.5
Radius of big circle = (s * 2^0.5)/2
Area of small circle = pi * radius^2 = pi * (s/2)^2
Area of small circle = pi * (s^2)/4
Area of big circle = pi * radius^2 = pi * [(s * 2^0.5)/2]^2 = pi * [((s^2) * 2)/4]
Area of big circle = pi * [(s^2)/2]
Ratio of Area of big circle to Area of small circle = [pi * (s^2)/2] / [pi * (s^2)/4]
After cancelling out pi and s^2, we get:
Ratio of Area of big circle to Area of small circle = 4 / 2 = 2
Therefore, the answer is D) 2.
Re: The figure above shows a circle inscribed in a square which
[#permalink]
02 Aug 2020, 06:14
02 Aug 2020, 06:14
1
radius of smaller circle = R
since outer of smaller circle is a square, 2 sides are R each, then other two sides are also R. Thus one full side is 2R.
Radius of larger circle = hypotenuse of R as radius and R as side
Thus radius of big circle is is = R^2 + R^2 = 2R^2 => Hyp = root 2 R.
Then we check for proportion --> pie (root 2*R^2)^2/ pie *(R)^2 = 2:1
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since outer of smaller circle is a square, 2 sides are R each, then other two sides are also R. Thus one full side is 2R.
Radius of larger circle = hypotenuse of R as radius and R as side
Thus radius of big circle is is = R^2 + R^2 = 2R^2 => Hyp = root 2 R.
Then we check for proportion --> pie (root 2*R^2)^2/ pie *(R)^2 = 2:1
Kudos if you like this post
