A rectangular park is 100 m by 50 m.

Question:

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).

Solution:

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 $0.60 \times 9812.5$

$=\operatorname{Rs} 5887.50 /-$

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