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 $32.40 \mathrm{~m}$.