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# If the area of a sector in a circle is x% of the total area of the cir

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Math Expert
Joined: 02 Sep 2009
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If the area of a sector in a circle is x% of the total area of the cir  [#permalink]

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13 Sep 2018, 04:05
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Difficulty:

55% (hard)

Question Stats:

63% (01:29) correct 38% (02:02) wrong based on 24 sessions

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If the area of a sector in a circle is x% of the total area of the circle, what is the measure of the corresponding central angle?

(1) The ratio of the perimeter of the sector to the circumference of the circle is $$\frac{2\pi + 5}{5\pi}$$.
(2) x = 40

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Re: If the area of a sector in a circle is x% of the total area of the cir  [#permalink]

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15 Sep 2018, 02:55
If the area of a sector in a circle is x% of the total area of the circle, what is the measure of the corresponding central angle?

(1) The ratio of the perimeter of the sector to the circumference of the circle is $$\frac{2π+5}{5π}$$

perimeter of the sector = $$2r+ rθ = r(2+central angle)$$
circumference central angle of the circle = $$2πr$$

$$\frac{r(2+θ)}{2πr} = \frac{(2π+5)}{5π}$$

$$5(2+θ) = 2(2π+5)$$
$$10+θ=4π+10$$$$θ = 4π$$
sufficient

(2) x = 40
im guessing 25% of the circle means central angle is 90 that is 25% of 360
50% of the circle means central angle is 180 that is 50% of 360
Sector occupies 40% of the total circle so central angle= 40/100*360 = 144
sufficient

Do let me know if the reasoning is right... thanks
Re: If the area of a sector in a circle is x% of the total area of the cir &nbs [#permalink] 15 Sep 2018, 02:55
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