Question
A rectangular park is $100\ m$ by 50m. 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 $\big(\text{Take }\pi=3.14\big).$
✓
Answer
Since four semicircular flower beds rounds the rectangular park. Then, diameters of semicircular.
plots are $2r_1 = l$ and $2r_2 = w$
So, the radius of semicircle at larger side of rectangle
$\text{r}_1=\frac{\text{l}}{2}$
$=\frac{100}{2}$
$=50\text{m}$
Area of semicicluar plot at larger side of rectangle $=\frac{1}{2}\pi\text{r}^2$
$=\frac{1}{2}\times3.14\times50\times50$
$=3925\text{m}^2$
And the radius of semicircle at smaller side of rectangle
$\text{r}_2=\frac{\text{l}}{2}$
$=\frac{50}{2}$
$=25\text{m}$
Area of semicicluar plot at samller side of rectangle $=\frac{1}{2}\pi\text{r}^2$
$=\frac{1}{2}\times3.14\times25\times25$
$=981.25\text{m}^2$
Now, the total area of semicircular plot is sum of area of four semicircular plots.
Total Area of plot $= 2 × 3925 + 2 × 981.25$
$= 7850 + 1962.5m^2$
$= 9812.5m^2$
Since, The cost of levelling semicircular flower bed per square meter $= Rs. 0.60$
So, The cost of levelling 9812.5 square meter flower bed $= Rs. 0.60 × 9812.5$
$= Rs. 5887.50$
plots are $2r_1 = l$ and $2r_2 = w$
So, the radius of semicircle at larger side of rectangle
$\text{r}_1=\frac{\text{l}}{2}$
$=\frac{100}{2}$
$=50\text{m}$
Area of semicicluar plot at larger side of rectangle $=\frac{1}{2}\pi\text{r}^2$
$=\frac{1}{2}\times3.14\times50\times50$
$=3925\text{m}^2$
And the radius of semicircle at smaller side of rectangle
$\text{r}_2=\frac{\text{l}}{2}$
$=\frac{50}{2}$
$=25\text{m}$
Area of semicicluar plot at samller side of rectangle $=\frac{1}{2}\pi\text{r}^2$
$=\frac{1}{2}\times3.14\times25\times25$
$=981.25\text{m}^2$
Now, the total area of semicircular plot is sum of area of four semicircular plots.
Total Area of plot $= 2 × 3925 + 2 × 981.25$
$= 7850 + 1962.5m^2$
$= 9812.5m^2$
Since, The cost of levelling semicircular flower bed per square meter $= Rs. 0.60$
So, The cost of levelling 9812.5 square meter flower bed $= Rs. 0.60 × 9812.5$
$= Rs. 5887.50$
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