Question

In the given figure, the ratio of the area of the shaded portion to the area of the total figure is ________.

• A. $2:3$
• B. $1:4$
• C. $1:2$
• D. $1:3$

Answer 1

The correct option is C $1:2$

$\Rightarrow$ In given figure, we can see there are three semi-circle.

$\Rightarrow$ Two same size small semi-circle and one large semi-circle.

$\Rightarrow$ Radius of small semi circle $=\frac{1}{2}\times 14=7cm$

$\Rightarrow$ Radius of large semi-circle $=\frac{1}{2}\times 28=14cm$

$\Rightarrow$ Area of two small semi-circle $=2(\frac{1}{2}\times \pi \times r^2)=2(\frac{1}{2}\times \frac{22}{7}\times (7{)}^2)=154c{m}^2$

$\Rightarrow$ Area of large semi circle $=\frac{1}{2}\times \pi \times r^2=\frac{1}{2}\times \frac{22}{7}\times (14{)}^2=308c{m}^2$

$\Rightarrow$ Area of the shaded portion $=(308-154)c{m}^{=}154c{m}^2$

$\therefore$ Required ratio $=\frac{154}{308}=\frac{1}{2}=1:2$