question_answer

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 .