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 $32.40\ m$.

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Updated on: 10-Oct-2022

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