Question:
A square tank has an area of 1600 cm2. There are four semicircular plots around it. Find the cost of turfing the plots at Rs 12.50 per m2.
Solution:
Let a m be the side of the square.
Area of the square $=a^{2}$
Thus, we have:
$a^{2}=1600$
$\Rightarrow a=40$
Area of the plots = 4(Area of the semicircle of radius 20 m)
$=\left|4\left(\frac{1}{2} \pi r^{2}\right)\right| \mathrm{m}^{2}$
$=\left|4\left(\frac{1}{2} \times 3.14 \times 20 \times 20\right)\right| \mathrm{m}^{2}$
$=2512 \mathrm{~m}^{2}$
$\therefore$ Cost of turfing the plots at $12.50$ per $\mathrm{m}^{2}=\mathrm{Rs}(2512 \times 12.50)$
$=$ Rs 31400