Question

In the given figure is made up of one big circle,two identical medium circles and two identical small circles.The ratio of the radius of the small circle to the radius of the medium circle is 2 : 3.
a) What is the total area of unshaded part in the figure?
b) What fraction of the bug circle is shaded?

• A. (a) $144\pi c{m}^2$ (b) $\frac{5}{18}$
• B. (a) $104\pi c{m}^2$ (b) $\frac{5}{18}$
• C. (a) $104\pi c{m}^2$ (b) $\frac{13}{18}$
• D. (a) $144\pi c{m}^2$ (b) $\frac{13}{18}$

Answer 1

The correct option is B (a) $104\pi c{m}^2$ (b) $\frac{5}{18}$

Let $r,\rho ,R$ be the radii of small, medium and big circles respectively.

Radius of small circle $=r=4cm$.

Radius of medium circle $=\rho =4\times \frac{3}{2}=6cm$. (small:medium=2:3)

Radius of big circle $=R=2\times 6=12cm$.

$\left(a\right)$ Area of unshaded part $=2\times \pi r^2+2\times \pi {\rho }^2=2\pi (4^2+6^2)=104\pi c{m}^2$

Area of big circle $=\pi R^2={12}^2\pi =144\pi$

Area of shaded part $=\pi R^2-104\pi =144\pi -104\pi =40\pi c{m}^2$

$\left(b\right)$ Fraction of area shaded $=\frac{40\pi }{144\pi }=\frac{5}{18}.$

$\therefore$ The answer is $\left[B\right]$.