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

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Joined: 02 Sep 2009
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A circle with a circumference of 12π is divided into three sectors wit  [#permalink]

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30 Oct 2018, 02:39
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Difficulty:

25% (medium)

Question Stats:

84% (01:35) correct 16% (01:48) wrong based on 30 sessions

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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

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Re: A circle with a circumference of 12π is divided into three sectors wit  [#permalink]

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30 Oct 2018, 02:44
Bunuel wrote:
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

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 $$= [\frac{5}{(3+4+5)}]*πr^2 = (\frac{5}{12})*π*6^2 = 15π$$

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A circle with a circumference of 12π is divided into three sectors wit  [#permalink]

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Updated on: 30 Oct 2018, 02:51
Circumference = 2πr = 12π.

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.

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Originally posted by Chethan92 on 30 Oct 2018, 02:47.
Last edited by Chethan92 on 30 Oct 2018, 02:51, edited 2 times in total.
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Re: A circle with a circumference of 12π is divided into three sectors wit  [#permalink]

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30 Oct 2018, 02:48
1
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
Re: A circle with a circumference of 12π is divided into three sectors wit   [#permalink] 30 Oct 2018, 02:48
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