Question

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

• A. 77

Answer 1

The correct option is A 77

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.

$Areaofthesemicirclea$ $=\frac{1}{2}\times \frac{22}{7}\times 7^2$
$=77{cm}^2$.

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
$=\frac{1}{2}\times \pi \times r^2$
$=\frac{1}{2}\times \frac{22}{7}\times {3.5}^2$
$=19.25{cm}^2$

$Theareaoftheshadedpart=Areaofsemicirclea+Areaofsemicircleb-Areaofthesemicirclec=77+19.25–19.25$
$=77c{m}^2$

The area of the shaded part is $77{cm}^2$