Question

In the adjoining figure, find the area of the shaded portion.

• A. $145$ $c{m}^2$
• B. $15.4$ $c{m}^2$
• C. $154$ $c{m}^2$
• D. $1.54$ $c{m}^2$

Answer 1

The correct option is C $154$ $c{m}^2$

Diameter of the larger semi-circle, $2R=28$ cm
$\therefore$ Its radius $R=14$ cm
Diameter of smaller semi-circle, $2r=14$ cm
Area of the shaded portion = (Area of large semi-circle) - 2 (Area of smaller semi-circle)
= $\frac{1}{2}\pi R^2-2\left(\frac{1}{2}\pi r^2\right)=\frac{1}{2}\pi (R^2-2r^2)$
= $\frac{1}{2}\times \frac{22}{7}|{14}^2-2(7{)}^2|=\frac{11}{7}(196-98)$
$\Rightarrow =\frac{11}{7}\left(98\right)=154c{m}^2$