A geometry problem by Niaz Ahmad

Geometry Level 3

The figure above shows a circle with center C and radius 6. What is the sum of the areas of the two shaded regions?

7.5 pi

6 pi

4.5 pi

4 pi

4.5 7.5 6 4

Niaz Ahmad by Niaz Ahmad , 28, Pakistan

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2 solutions

Mohamed Ehab
Aug 31, 2015

the area of shaded part is a percentage of the total area Percentage = (360-160 2)/360 = 40/360 =1/9 Area of Circle = pi r^2 = pi * 6^2 = 36 Pi Area of shaded = 1/9 *36 Pi = 4 Pi

1 Helpful 0 Interesting 2 Brilliant 3 Confused

Consider the diagram on the left.

The central angle of each of the shaded sector is 360 − 160 − 160 2 = 2 0 ∘ \dfrac{360-160-160}{2}=20^\circ .

Since the shaded part is composed of two equal sectors, we have

A = 2 ( θ 360 ) π r 2 = 2 ( 20 360 ) ( π ) ( 36 ) = 4 π A=2\left(\dfrac{\theta}{360}\right)\pi r^2=2\left(\dfrac{20}{360}\right)(\pi)(36)=4 \pi

3 Helpful 1 Interesting 0 Brilliant 9 Confused

4pi is what should be the answer, but it says that it is wrong. Can someone explain why

Rohan sunny - 1 year, 2 months ago

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