Question

A park is in the form of a rectangle 120 m by 90 m. At the centre of the park there is a circular lawn as shown in the figure. The area of the park excluding the lawn is 2950 m². Find the radius of the circular lawn.

Answer 1

Area of the rectangle = $l\times b$
$$\begin{gathered} =120\times 90 \\ =10800\mathrm{sq}.\mathrm{m} \end{gathered}$$

Area of the park excluding the lawn = 2950 m²

Area of the circular lawn = Area of the park $-$ Area of the park excluding the lawn
= 10800 $-$ 2950
= 7850 m²
Area of the circular lawn = $\mathrm{\pi }{r}^2$
$$\begin{gathered} \Rightarrow 7850=\frac{22}{7}\times r^2 \\ \Rightarrow \frac{7850\times 7}{22}=r^2 \\ \Rightarrow r^2=2497.72 \\ \Rightarrow r=49.97 \\ \mathrm{Or}, \\ r\approx 50\mathrm{m} \end{gathered}$$

Thus, the radius of the circular lawn is 50 m.