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 $c{m}^2$
• B. 94.54$c{m}^2$
• C. 98.12 $c{m}^2$
• D. 100.57 $c{m}^2$

Answer 1

The correct option is D

100.57 $c{m}^2$

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 =$\frac{1}{2}\times \frac{22}{7}\times 8^2$ = 100.57 ${cm}^2$.

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 =$\frac{1}{2}\times \pi \times r^2$ = $\frac{1}{2}\times \frac{22}{7}\times 4^2$ = 25.14 ${cm}^2$

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 $c{m}^2$

The area of the shaded part is 100.57 ${cm}^2$.