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# In the figure below, O is the center of the circle that has a radius o

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Math Expert
Joined: 02 Sep 2009
Posts: 49968
In the figure below, O is the center of the circle that has a radius o  [#permalink]

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05 Oct 2018, 00:09
00:00

Difficulty:

15% (low)

Question Stats:

95% (00:42) correct 5% (02:12) wrong based on 20 sessions

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In the figure below, O is the center of the circle that has a radius of 2 units. If the area of the sector containing the angle p° is π/2, what is the value of p in degrees?

(A) 15.0
(B) 30.0
(C) 45.0
(D) 60.0
(E) 75.0

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2018-10-05_1108.png [ 7.03 KiB | Viewed 203 times ]

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Re: In the figure below, O is the center of the circle that has a radius o  [#permalink]

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05 Oct 2018, 00:17
R= 2
(Theta/360)*pi*r^2 = pi/2

Theta = 45°
C

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Re: In the figure below, O is the center of the circle that has a radius o  [#permalink]

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06 Oct 2018, 16:31
Formula to calculate area of sector, angle of sector and length of arc

$$\frac{Angle at arc}{360}$$ = $$\frac{area of sector}{area of circle}$$ = $$\frac{length of Arc}{2\pi r}$$

We will use this $$\frac{Angle at arc}{360}$$ = $$\frac{area of sector}{area of circle}$$

$$\frac{p^o}{360}$$ = $$\frac{\pi}{2}$$*$$\frac{1}{2 \pi 2}$$

On simplification we get $$p^o = 45^o$$

* application of formula tag replaces spaces between strings. Don't know how to correct this.

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Re: In the figure below, O is the center of the circle that has a radius o &nbs [#permalink] 06 Oct 2018, 16:31
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