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12 Jul 2020, 08:17
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C
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Difficulty:
45%
(medium)
Question Stats:
69% (02:31) correct
31%
(03:28)
wrong
based on 71
sessions
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Attachment:
Screenshot 2020-07-12 at 8.47.48 PM.png [ 11.04 KiB | Viewed 3038 times ]
A. 4π
B. 6π
C. 12π
D. 16π
E. 26π
alternate to an easier version herel
12 Jul 2020, 09:08
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Kritisood
Let the radius be:
R3, R2, R1 such that R3 > R2 > R1
R3 = 2*R2
R2 = 2*R1
=> R3 = 4R1
Area of shaded region = \(\pi\) * [(R2)^2 - (R1)^2] = \(\pi\) * [(2*R1)^2 - (R1)^2] = \(\pi\) * 3 * (R1)^2
Area of largest circle = \(\pi\) * (R3)^2 = \(\pi\) * 16 * (R1)^2
Difference between the areas = \(\pi\) * [16 * (R1)^2 - 3 * (R1)^2] = 52*\(\pi\)
=> 13*(R1)^2 = 52
=> R1 = 2
=> R2 = 4
=> R3 = 8
Area of shaded region = \(\pi\) * 3 * (R1)^2 = \(\pi\) * 3 * (2)^2 = \(\pi\) * 12
Answer: C
12 Jul 2020, 09:37
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Let the radius of smallest circle be X, then the radii of smaller circle will be 2X and large circle will be 4X.
Given that π*(4X)^2 = π*(2X)^2 - π*(X)^2 + 52π
=> 13*π*X^2 = 52π
=> X = 2
So, area of shaded part = π*(2X)^2 - π*(X)^2
=> 3*π*X^2
=> 12π
OA: C
Posted from my mobile device
Given that π*(4X)^2 = π*(2X)^2 - π*(X)^2 + 52π
=> 13*π*X^2 = 52π
=> X = 2
So, area of shaded part = π*(2X)^2 - π*(X)^2
=> 3*π*X^2
=> 12π
OA: C
Posted from my mobile device
