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In the figure to the right, circle P has diameter 2 and circle Q has
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Author:  Bunuel [ 17 Jun 2017, 05:10 ]
Post subject:  In the figure to the right, circle P has diameter 2 and circle Q has

In the figure to the right, circle P has diameter 2 and circle Q has diameter 1. What is the area of the shaded region?



(A) 3/4*π
(B) 3π
(C) 7/2*π
(D) 5π
(E) 6π

Attachment:
2017-06-17_1708.png
2017-06-17_1708.png [ 14.46 KiB | Viewed 6048 times ]


Source: Nova GMAT
Difficulty Level: 550

Author:  BrentGMATPrepNow [ 17 Jun 2017, 07:19 ]
Post subject:  In the figure to the right, circle P has diameter 2 and circle Q has

Bunuel wrote:
In the figure to the right, circle P has diameter 2 and circle Q has diameter 1. What is the area of the shaded region?



(A) 3/4*π
(B) 3π
(C) 7/2*π
(D) 5π
(E) 6π

Attachment:
2017-06-17_1708.png


Circle P: diameter 2
So, the radius (r) = 1


Circle Q: diameter 1
So, the radius (r) = 1/2


area of circle = πr²

SHADED area = (area of circle P) - (area of circle Q)
We get: SHADED area = (π)(1²) - (π)(1/2
= (π)(1) - (π)(1/4)
= π(1 - 1/4)
= π(3/4)

Answer: A

Author:  pushpitkc [ 17 Jun 2017, 05:14 ]
Post subject:  Re: In the figure to the right, circle P has diameter 2 and circle Q has

Since the outer circle has diameter 2, radius is 1 and area of the circle = \(π * 1^2 = π\)
Similarly the inner circle has diameter 1, radius is 1/2 and area of the inner circle is \(π *(1/2)^{2} = π/4\)

Hence, area of shaded region = area of outer circle - area of inner circle = 3/4 * π(Option A)

Author:  Abhishek009 [ 17 Jun 2017, 07:44 ]
Post subject:  Re: In the figure to the right, circle P has diameter 2 and circle Q has

\(D = 2\) and \(d = 1\)

So, \(R = 1\) and \(r = \frac{1}{2}\)

Area of the shaded region is \(π(R^2 - r^2)\)

Or, Area of the shaded region is \(π(1 - 1/4)\)

Or, Area of the shaded region is \(\frac{3π}{4}\)

Hence, the correct answer must be (A)

Author:  bumpbot [ 20 Nov 2022, 02:40 ]
Post subject:  Re: In the figure to the right, circle P has diameter 2 and circle Q has

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