Find the ratio between the area of the shaded and the unshaded portions of the following figure :

Let r be the radius of the given circle.

Let l and b be the length and breadth of the rectangle.

l = r + 2r = 3r

b = 2r

Area of rectangle = l x b

= 3r x 2r

= 6r²

Area of shaded portion = Area of circle + Area of semicircle

= πr² + $\dfrac{1}{2}$πr²

= $\dfrac{3}{2}$ πr²

= $\dfrac{3}{2} \times \dfrac{22}{7}$ r²

= $\dfrac{66}{14}$ r²

= $\dfrac{33}{7}$ r²

Area of the unshaded portion = Area of rectangle - Area of shaded portion

= 6r² - $\dfrac{33}{7}$ r²

= $\dfrac{42}{7}$ r² - $\dfrac{33}{7}$ r²

= $\dfrac{9}{7}$ r²

The ratio between the area of the shaded and the unshaded portions

$= \dfrac{\dfrac{33}{7}r^2}{\dfrac{9}{7}r^2}\\[1em] = \dfrac{\dfrac{33}{7}}{\dfrac{9}{7}}\\[1em] = \dfrac{33}{9}\\[1em] = \dfrac{11}{3}$

Hence, the ratio between the area of the shaded and the unshaded portions = 11:3.