A park is in the form of a rectangle 120 m × 100 m.

Question:

A park is in the form of a rectangle 120 m × 100 m. At the centre of the park there is a circular lawn, The area of park excluding lawn is 8700 m2. Find the radius of the circular lawn. (Use π = 22/7).

Solution:

Let the radius of circular lawn be r. Then,

Area of circular lawn $=\pi r^{2}$

It is given that

Area of park excluding lawn $=$ Area of rectangle-Area of circular lawn

$8700=120 \times 100-\pi r^{2}$

$\pi r^{2}=12000-8700$

$\frac{22}{7} r^{2}=3300$

$r^{2}=\frac{3300 \times 7}{22}$

$r^{2}=1050$

$r=\sqrt{1050}$

$r=32.40 \mathrm{~m}$

Hence, radius of circular lawn is $32.40 \mathrm{~m}$.

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