Question

In the above figure, if shaded portion has been cut-out from a circle A of diameter 112 cm and centre O. Then, the area of the remaining part of the circle is equal to ___

• A. 3 times area of shaded figure
• B. 2 times area of shaded figure
• C. area of shaded figure
• D. none of these

Answer 1

The correct option is A 3 times area of shaded figure


Given diameter of the circle is 112 cm.
Area of the circle $\pi \times {56}^2$

Calculating the area of shaded region we find that it is,
$\Rightarrow 2\times [(\frac{\pi \times {28}^2}{2}-\frac{\pi \times {14}^2}{2})+\frac{\pi \times {14}^2}{2}]$
$\Rightarrow 2\times \left[\frac{\pi \times {28}^2}{2}\right]$
$\Rightarrow \pi \times {28}^2$

Area of the remaining circle $=(\pi \times {56}^2)-(\pi \times {28}^2)$

$\frac{\text{Area of the remaining circle}}{\text{Area of the shaded region}}=\frac{(\pi \times {56}^2)-(\pi \times {28}^2)}{(\pi \times {28}^2)}$
$=\frac{\pi \times {56}^2}{\pi \times {28}^2}-1$
$=\frac{\pi \times 2^2\times {28}^2}{\pi \times {28}^2}-1$
$=4-1=3$
$\therefore$ Area of the remaining circle = 3 x Area of the shaded region