In the figure shown, if the radius of circle P is 3 times the radius

Question

https://gmatclub.com/forum/download/file.php?id=58593 In the figure shown, if the radius of circle P is 3 times the radius of circle A, ∠BAC = ∠QPR, and the shaded area of circle A is 3\pi square units, then what is the area of the shaded part of circle P? A. 9\pi B. 12\pi C. 15\pi D. 21\pi E. 27\pi Project PS Butler Subscribe to get Daily Email - Click Here | Subscribe via RSS - RSS 2020-10-27_12-53-53.png

rajatchopra1994 · Answer

Explanation:
Let radius of circle A is r , so Cicle P radius will be 3r
Area of Circle A is = πr^2
Area of Circle P is = π(3r)^2 = 9πr^2

Ratio will be 1:9

so angle is same between two arc of circle, so area PQR will be = 3π*9 = 27π

IMO-E

SairamRamo · Answer

X - Circle ABC radius
Y- Circle PQR radius

Given Y = 3X

Area of ABC shaded region = shaded region fraction * area of circle ABC = shaded region fraction * PI * X^2 = 3*PI (given)

Area of PQR shaded region = shaded region fraction * area of circle PQR = shaded region fraction * PI * Y^2 = shaded region fraction * PI * X^2 * 9 = 3 * pi * 9 = 27 * pi

IMO E

GCMEMBER · Answer

In the figure shown, if the radius of circle P is 3 times the radius of circle A, ∠BAC = ∠QPR, and the shaded area of circle A is \(3\pi\) square units, then what is the area of the shaded part of circle P?

A. \(9\pi\)
B. \(12\pi\)
C. \(15\pi\)
D. \(21\pi\)
E. \(27\pi\)

Circle A
shaded area = (∠BAC/360)*πr^2 = 3π

Circle P
shaded aera = (∠QPR/360)*π(3r^2)
= 9*(∠BAC/360)*πr^2
= 9*3π
= 27π

Option E

QuantMadeEasy · Answer

Step 1: Understanding the question 
Ratio of radii =  \frac{Radius of Circle A }{ Radius of Circle P} = \frac{1}{3} 
As central angle is same:
Ratio of sector areas =  \frac{Area Of Sector ABC }{ Area Of Sector PQR} = \frac{(Radius Of Circle A)^2 }{ (Radius Of Circle P)^2} = \frac{1}{9}

Step 2: Calculation  
When Area of sector ABC is 1 unit, Area of sector PQR is 9 units
When Area of sector ABC is 3π unit, Area of sector PQR is 9*3π = 27π units

E is correct

ScottTargetTestPrep · Answer

Solution:

Since circle P’s radius is 3 times circle A’s radius, its area is 3^2 = 9 times circle A’s area. Since angle BAC = angle QPR, the area of the shaded region of circle P will be also 9 times the area of the shaded region of circle A. Therefore, the area of the shaded region of circle P is 9 x 3π = 27π.

Answer: E

In the figure shown, if the radius of circle P is 3 times the radius

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In the figure shown, if the radius of circle P is 3 times the radius

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