A rectangular park is 100 m by 50 m. It is surrounding by semi-circular flower beds all round. Find the cost of levelling the semi-circular flower beds at 60 paise per square metre (use π = 3.14).
Since four semicircular flower beds rounds the rectangular park. Then, diameters of semicircular plots are $2 r_{1}=l$ and $2 r_{2}=w$
So, the radius of semicircle at larger side of rectangle
$r_{1}=\frac{l}{2}$
$=\frac{100}{2}$
$=50 \mathrm{~m}$
Area of semicircluar plot at larger side of rectangle $=\frac{1}{2} \pi r^{2}$
$=\frac{1}{2} \times 3.14 \times 50 \times 50$
$=3925 \mathrm{~m}^{2}$
And the radius of semicircle at smaller side of rectangle
$r_{2}=\frac{l}{2}$
$=\frac{50}{2}$
$=25 \mathrm{~m}$
Area of semicircluar plot at smaller side of rectangle $=\frac{1}{2} \pi r^{2}$
$=\frac{1}{2} \times 3.14 \times 25 \times 25$
$=981.25 \mathrm{~m}^{2}$
Now, the total area of semicircular plot is sum of area of four semicircular plots.
Total Area of plot $=2 \times 3925+2 \times 981.25$
$=7850+1962.5 \mathrm{~m}^{2}$
$=9812.5 \mathrm{~m}^{2}$
Since, The cost of levelling semicircular flower bed per square meter $=\operatorname{Rs} 0.60$
So, The cost of levelling $9812.5$ square meter flower bed $=$ Rs $0.60 \times 9812.5$
$=\operatorname{Rs} 5887.50 /-$