Question

If the larger circle of radius $14cm$ has four smaller circles of radius $3.5cm,$ then the area of the shaded portion is

• A. $400c{m}^2$
• B. $426c{m}^2$
• C. $462c{m}^2$
• D. $482c{m}^2$

Answer 1

The correct option is C

$462c{m}^2$

Let the radius of bigger circle be $r_1$ and

radius of smaller circles be $r_2$

So, $r_1=14cm$ and $r_2=3.5cm$
Area of shaded portion $=$ area of the bigger circle $-$ area of smaller circles

$=\pi r_1^2-4\pi r_2^2$
$=\pi ({14}^2-4\times {3.5}^2)=\pi (196-49)=\frac{22}{7}\times 147=462c{m}^2$