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In the circle above, the length of arc AB is 3π. If the circle has an

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Joined: 02 Sep 2009
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In the circle above, the length of arc AB is 3π. If the circle has an  [#permalink]

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17 Jan 2019, 04:24
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Question Stats:

73% (01:49) correct 27% (01:28) wrong based on 64 sessions

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In the circle above, the length of arc AB is 3π. If the circle has an area of 16π, what is the measure of central angle AOB?

A 45

B 67.5

C 95

D 115

E 135

Attachment:

2019-01-17_1523.png [ 9.66 KiB | Viewed 783 times ]

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In the circle above, the length of arc AB is 3π. If the circle has an  [#permalink]

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17 Jan 2019, 04:38
Bunuel wrote:

In the circle above, the length of arc AB is 3π. If the circle has an area of 16π, what is the measure of central angle AOB?

A 45

B 67.5

C 95

D 115

E 135

Attachment:
2019-01-17_1523.png

Length of Arc AB=3π=2πr*(Angle AOB/2π)=r* Angle AOB---(1)

Given Area of circle=16π
Or, $$π*r^2=16π$$
Or, $$r^2=16$$
Or, $$r=4$$

Now from(1), we have Angle AOB=3π/4=135 degree

Ans. (E)
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Re: In the circle above, the length of arc AB is 3π. If the circle has an  [#permalink]

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17 Jan 2019, 07:03

Solution

Given:
• Length of arc AB = 3ᴨ
• Area of circle = 16ᴨ

To find:
• Angle AOB

Approach and Working:
Length of arc AB = $$\frac{x}{360} * 2ᴨ * r$$, where,
• x = angle AOB

• Therefore, $$x = \frac{3ᴨ * 360}{2ᴨ * 4} = 135$$ degrees

Hence, the correct answer is Option E

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Re: In the circle above, the length of arc AB is 3π. If the circle has an  [#permalink]

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17 Jan 2019, 08:38
Bunuel wrote:

In the circle above, the length of arc AB is 3π. If the circle has an area of 16π, what is the measure of central angle AOB?

A 45

B 67.5

C 95

D 115

E 135

Attachment:
2019-01-17_1523.png

angle /360 * 2* pi * r = 3 pi
and pi * r2 = 16 pi
r = 4
angle = 540/4
= 135
IMO E
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Re: In the circle above, the length of arc AB is 3π. If the circle has an  [#permalink]

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21 Jan 2019, 19:14
Bunuel wrote:

In the circle above, the length of arc AB is 3π. If the circle has an area of 16π, what is the measure of central angle AOB?

A 45

B 67.5

C 95

D 115

E 135

Attachment:
2019-01-17_1523.png

Since the area of the circle is 16π, the radius is 4, and the circumference is 2 x π x 4 = 8π.

Since arc AB has a length of 3π, the central angle is 3π/8π x 360 = 3/8 x 360 = 3 x 45 = 135 degrees.

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In the circle above, the length of arc AB is 3π. If the circle has an  [#permalink]

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24 Jan 2019, 12:30
Bunuel wrote:

In the circle above, the length of arc AB is 3π. If the circle has an area of 16π, what is the measure of central angle AOB?

A 45

B 67.5

C 95

D 115

E 135

My thought process if it helps anyone:

Area = 16pi means radius = 4

This means the perimeter of the circle is 8pi.

The ratio of the angle to 360 will equal to the ratio of the length of the arc to the entire perimeter.

$$\frac{3pi}{8pi} = \frac{x}{360}$$

x= 135
In the circle above, the length of arc AB is 3π. If the circle has an   [#permalink] 24 Jan 2019, 12:30
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