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In the figure above, an unshaded circle with diameter x is surrounded

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In the figure above, an unshaded circle with diameter x is surrounded  [#permalink]

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New post 23 Jun 2020, 05:25
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A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

33% (02:53) correct 67% (02:36) wrong based on 18 sessions

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In the figure above, an unshaded circle with diameter x is surrounded by a shaded region with uniform width of 2. For which of the following values of x is the area of the unshaded circle greater than the area of the shaded region?

I. 9
II. 10
III. 11

A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III

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In the figure above, an unshaded circle with diameter x is surrounded  [#permalink]

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New post 23 Jun 2020, 05:47
Given: An unshaded circle with diameter x is surrounded by a shaded region with uniform width of 2.

To find: For which of the following values of x is the area of the unshaded circle greater than the area of the shaded region?

Solution. : x/2 = r
Area of unshaded region = πr^2
Area of shaded region = π(r+2)^2 - πr^2

Au > As
πr^2 > π(r+2)^2 - πr^2
2πr^2 > π(r+2)^2
2r^2 > (r+2)^2

1. 9 => radius = 4.5
2r^2 > (r+2)^2
2(4.5)^2 > (4.5+2)^2
2*20.25 > 6.5^2
40.5 < 42.25 (not satisfying)

2. 10 => radius = 5
2r^2 > (r+2)^2
2(5)^2 > (5+2)^2
2*25 > 7^2
50 > 49 (satisfying)

3. 11 => radius = 5.5
2r^2 > (r+2)^2
2(5.5)^2 > (5.5+2)^2
2*30.25 > 7.5^2
60.5 > 56.25 (satisfying)

Therefore only 2&3 values are statisfying.

Answer is D

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In the figure above, an unshaded circle with diameter x is surrounded   [#permalink] 23 Jun 2020, 05:47

In the figure above, an unshaded circle with diameter x is surrounded

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