A park is in the form of a rectangle of dimensions\[120\,m\times 100\,m\]. In the centre of the park, there is a circular lawn as shown in the figure. The area of the park excluding the lawn is \[8700\,{{m}^{2}}\]. Find the radius of the circular lawn. |
A) \[32.4\,m\]
B) \[36\,m\]
C) \[29.6\,m\]
D) \[39.4\,m\]
Correct Answer: A
Solution :
[a] Area of park \[=120\times 100{{m}^{2}}=12000{{m}^{2}}\] |
Let radius of lawn \[=\text{r m}\] |
\[\therefore \] Area of lawn \[=\pi {{r}^{2}}{{m}^{2}}\] |
\[\therefore \] Area of park excluding the lawn |
\[=(12000-\pi {{r}^{2}}){{m}^{2}}\] |
By the given condition, \[12000-\pi {{r}^{2}}=8700\] |
\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\pi {{r}^{2}}=12000-8700=3300\] |
\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,{{r}^{2}}=\frac{3300}{\pi }=\frac{3300}{22}\times 7=1050\] |
\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,r=\sqrt{1050}=32.4\] |
Hence, radius of circular lawn is . |
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