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D
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Difficulty:
75%
(hard)
Question Stats:
35% (01:46) correct
65%
(02:22)
wrong
based on 37
sessions
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A circle is inscribed in a square which is further inscribed in another circle. What is the approximate area of the circle that is not occupied by another circle?
(1) Difference between circumferences of both circles is 1.3 cm
(2) Difference between diagonal and side of a square is \(\sqrt{2}-1\) cm
(1) Difference between circumferences of both circles is 1.3 cm
(2) Difference between diagonal and side of a square is \(\sqrt{2}-1\) cm
globaldesi
Joined: 28 Jul 2016
Last visit: 23 Feb 2026
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Concentration: Finance, Human Resources
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18 Apr 2021, 21:01
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can you explain why B is not correct
given diagonal and side diff =\( \sqrt{2} -1\)
side will actually be diameter of smaller circle and diagonal will be diameter of bigger circle
So let side be s
then
\(\sqrt{2}s -s \)= \( \sqrt{2} -1\)
or s = 1
thus radius of inner circle is 0.5 and outer circle is \sqrt{2}*.5
We can now find percentage differce.
Can you help me understand what did I miss
given diagonal and side diff =\( \sqrt{2} -1\)
side will actually be diameter of smaller circle and diagonal will be diameter of bigger circle
So let side be s
then
\(\sqrt{2}s -s \)= \( \sqrt{2} -1\)
or s = 1
thus radius of inner circle is 0.5 and outer circle is \sqrt{2}*.5
We can now find percentage differce.
Can you help me understand what did I miss
19 Apr 2021, 01:11
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globaldesi
Let the radius of larger circle = r1, radius of smaller circle = r2, diagonal of square = d, side length of square = s and d = s\(\sqrt{2}\\
\)
We know that, diagonal of square = diameter of larger circle
=> d = 2 * r1
We also know that side length of square = diameter of smaller circle
=> s = 2 * r2
We want\( πr1^2 - πr2^2 = π * (r1^2 - r2^2)\)
Statement 1:
2πr1 - 2πr2 = 1.3 cm
=> \(2r1 - 2r2 = d - s = s\sqrt{2} - s = \frac{1.3}{2π}\approx\) 0.207
From this we can calculate s, d, r1 and r2, and can easily calculate \(πr1^2 - πr2^2\)
Statement 1 is Sufficient.
Statement 2:
\(d - s = \sqrt{2} - 1\)
=> \(d - s = s\sqrt{2} - s \sqrt{2} - 1\)
=> s = 1
From this we can calculate d, r1 and r2, and can easily calculate \(πr1^2 - πr2^2\)
Statement 2 is also Sufficient.
So, correct answer is option D.
