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Question

The Yin-Yang symbol can be explained by the following dimensions. What would be the area covered by the Yin (black) region if the radius of the larger circle is, R = 8 cm?



A

97.75 cm2

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B

94.54 cm2

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C

98.12 cm2

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D

100.57 cm2

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Solution

The correct option is D

100.57 cm2


Here we are asked to find the area of the shaded part. The figure can be split into 3 semicircle i.e. a, b and c in order to find the area.

 Area of the semicircle a =12×227×82 = 100.57 cm2


The diameter of semicircles b and c is equal to the radius of the semicircle a.Therefore the area of both the semicircles will be the same.

Area of the semicircle =12×π×r2  = 12×227×42 = 25.14 cm2

The area of the shaded part = Area of semicircle a + Area of semicircle b –  Area of the semicircle c = 100.57 +25.14 – 25.14 = 100.57 cm2

The area of the shaded part is 100.57 cm2.


Mathematics

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