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# If in the circle shown above with center O the area of the sector encl

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Math Expert
Joined: 02 Sep 2009
Posts: 53060
If in the circle shown above with center O the area of the sector encl  [#permalink]

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06 Sep 2018, 00:05
00:00

Difficulty:

25% (medium)

Question Stats:

80% (01:26) correct 20% (02:23) wrong based on 32 sessions

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If in the circle shown above with center O the area of the sector enclosed by AOB is 32π and the circle has radius 12, what is the measure of the angle AOB in degrees?

A. 90
B. 80
C. 75
D. 50
E. 45

Attachment:

image038 (1).jpg [ 1.79 KiB | Viewed 505 times ]

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Re: If in the circle shown above with center O the area of the sector encl  [#permalink]

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06 Sep 2018, 02:00
Bunuel wrote:

If in the circle shown above with center O the area of the sector enclosed by AOB is 32π and the circle has radius 12, what is the measure of the angle AOB in degrees?

A. 90
B. 80
C. 75
D. 50
E. 45

Attachment:
image038 (1).jpg

Area of sector = (angle/360)*2πr^2 i.e. (angle/360)*π12^2 = 32π (given)

i.e. Angle = 360*(32/144) = 80

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Re: If in the circle shown above with center O the area of the sector encl  [#permalink]

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06 Sep 2018, 03:11
(Length of arc) / (circumference of circle = (area of arc) / (area of circle) = angle made by arc/360

area of arc = $$32 \pi$$
area of circle = $$\pi * 12 ^ 2$$
angle made by arc = x

$$(32 \pi)/( \pi * 12 ^2) = x / 360$$
x = 80

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Re: If in the circle shown above with center O the area of the sector encl  [#permalink]

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06 Sep 2018, 06:27
Bunuel wrote:

If in the circle shown above with center O the area of the sector enclosed by AOB is 32π and the circle has radius 12, what is the measure of the angle AOB in degrees?

A. 90
B. 80
C. 75
D. 50
E. 45

Attachment:
image038 (1).jpg

$$\frac{θ}{360}*π*12*12 = 32π$$

Or, $$\frac{θ}{360}*3*3 = 2$$

Or, $$\frac{θ}{40} = 2$$

So, $$θ = 80°$$, Answer must be (B)
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If in the circle shown above with center O the area of the sector encl  [#permalink]

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06 Sep 2018, 16:34
Bunuel wrote:

If in the circle shown above with center O the area of the sector enclosed by AOB is 32π and the circle has radius 12, what is the measure of the angle AOB in degrees?

A. 90
B. 80
C. 75
D. 50
E. 45

Attachment:
image038 (1).jpg

Sector area is determined by the sector's central angle as a portion of the circle's 360°. Work backwards from area.

Radius = $$12$$
Area of circle: $$\pi r^2=\pi *12^2=144\pi$$

$$\frac{SectorArea}{CircleArea}=\frac{SectorAngle}{360°}$$

Let sector angle = $$x$$

$$\frac{32\pi}{144\pi}=\frac{x}{360}$$

$$(144)(x)=(32)(360)$$ - divide by 16

$$9x=(2)(360)$$ - divide by 9

$$x=(2)(40)=80$$

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If in the circle shown above with center O the area of the sector encl   [#permalink] 06 Sep 2018, 16:34
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