A circle with a circumference of 12π is divided into three sectors wit

Question

A circle with a circumference of 12π is divided into three sectors with areas in a ratio of 3:4:5. What is the area of the largest sector?

A. 6π
B. 9π
C. 12π
D. 15π
E. 18π

GMATinsight · Answer

Given:

Circumference of Circle = 2*π*r = 12π

i.e. radius of circle,  r = 6

Ratio of areas of three sectors = 3:4:5

i.e. Area of Largest sector  =  *πr^2 = (\frac{5}{12})*π*6^2 = 15π

Answer: Option D

Chethan92 · Answer

Circumference = 2πr = 12π.
Radius = 6.

Area of the circle  = πr^2 = 36π

Area is divided in the ratio 3:4:5

Area of the largest ratio = 5/12*36π = 15π.

D is the answer.

philipssonicare · Answer

Two parts to this question

1. Find the area of the circle

The shortcut formula is

A= \frac{c^2}{2π}

A= \frac{(12π)^2}{4π} 
A= \frac{144π^2}{4π}  =36π

The longer way to do this is:
Circumference = 2πr
12π=2πr
r=6

A= πr^2 
A= π6^2 =36π

2. Divide this up
The areas are in the ratio of 3:4:5
That is a total 12

\frac{36π}{12} =3π
5·3π=15π

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