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

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

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New post 30 Oct 2018, 01:39
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A
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C
D
E

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  25% (medium)

Question Stats:

75% (01:09) correct 25% (01:33) wrong based on 24 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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New post 30 Oct 2018, 01:44
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 \(= [\frac{5}{(3+4+5)}]*πr^2 = (\frac{5}{12})*π*6^2 = 15π\)

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

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New post Updated on: 30 Oct 2018, 01:51
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.
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Originally posted by Afc0892 on 30 Oct 2018, 01:47.
Last edited by Afc0892 on 30 Oct 2018, 01:51, 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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New post 30 Oct 2018, 01:48
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
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Re: A circle with a circumference of 12π is divided into three sectors wit &nbs [#permalink] 30 Oct 2018, 01:48
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