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A park is in the form of a rectangle $120\ m \times 100\ m$. At the centre of the park there is a circular lawn. The area of park excluding lawn is $8700\ m^2$. Find the radius of the circular lawn. (Use $\pi = \frac{22}{7}$).
Given:
A park is in the form of a rectangle $120\ m \times 100\ m$. At the centre of the park there is a circular lawn. The area of park excluding lawn is $8700\ m^2$.
To do:
We have to find the radius of the circular lawn.
Solution:
Area of the park excluding lawn$ = 8700\ m^2$
Length of the rectangular park $= 120\ m$
Width of the rectangular park $= 100\ m$
Area of a rectangle of length $l$ and breadth $b$ is $lb$.
This implies,
Area of the park $= 120 \times 100\ m^2$
$= 12000\ m^2$
Let $r$ be the radius of the circular lawn.
Area of the lawn $= \pi r^2$
Therefore,
$\pi r^{2}=12000-8700$
$\Rightarrow \frac{22}{7} r^{2}=3300$
$\Rightarrow r^{2}=\frac{3300 \times 7}{22}$
$\Rightarrow r^{2}=150 \times 7$
$\Rightarrow r^{2}=1050$
$\Rightarrow r=\sqrt{1050}$
$\Rightarrow r=32.40 \mathrm{~m}$
The radius of the circular lawn is $32.40\ m$.