Question

In figure there are three semicircles, A, B and C having diameter $3cm$ each, and another semicircle E having a circle D with diameter $4.5$cm are shown. Calculate:
(i) the area of the shaded region
(ii)the cost of painting the shaded region at the rate of $25$paise per $c{m}^2$, to the nearest rupee.

• A. $49.123m^2$, Rs. $6$
• B. $38.426c{m}^2$, Rs. $5$
• C. $26.846c{m}^2$, Rs. $4$
• D. $12.375c{m}^2$, Rs. $3$

Answer 1

The correct option is D $12.375c{m}^2$, Rs. $3$

Area of shaded region $=$ Area of larger semicircle $-$ Area of circle with center D

$-2$ (Area of small semi-circle)

$+$Area of small semi-circle

$=\frac{\pi }{2}{\left(4.5\right)}^2-\pi {\left(\frac{4.5}{2}\right)}^2$ - area of small semi-circle

$=\frac{\pi }{2}{\left(4.5\right)}^2-\pi {\left(\frac{4.5}{2}\right)}^2-\frac{\pi }{2}{\left(\frac{3}{2}\right)}^2$

$=\pi [{\frac{\left(4.5\right)}{2}}^2-{\left(\frac{4.5}{2}\right)}^2-\frac{1}{2}{\left(\frac{3}{2}\right)}^2]$

$=\pi \times 3.9375=12.375{cm}^2$

Cost of painting $=$ Rs. $(12.375\times 0.25)\approx Rs.3$