Question

In fig three semicircle of diameters $AB=8cm,BC=4cm$ and $CD=2cm$ are drawn.

Find area of shaded portion. $(\text{Take}\pi =\frac{22}{7})$

• A. $132c{m}^2$
• B. $42c{m}^2$
• C. $33c{m}^2$
• D. $21c{m}^2$

Answer 1

The correct option is C $33c{m}^2$

Area of shaded region $=$ Area of semi circle $AB+$ Area of semi circle $BC+$ Area of semi circle $CD$
$=\frac{\pi {\left(\frac{AB}{2}\right)}^2}{2}+\frac{\pi {\left(\frac{BC}{2}\right)}^2}{2}+\frac{\pi {\left(\frac{CD}{2}\right)}^2}{2}$
$=\frac{\pi {\left(\frac{8}{2}\right)}^2+\pi {\left(\frac{4}{2}\right)}^2+\pi {\left(\frac{2}{2}\right)}^2}{2}$
$=\frac{16\pi +4\pi +\pi }{2}$
$=\frac{21\pi }{2}$
$=\frac{21\times 22}{2\times 7}$
$=33c{m}^2$