Question:
A road which is 7 m wide surrounds a circular park whose circumference is 352 m. Find the area of the road.
Solution:
It is given that the circumference C of circular track is 352 m.
We know that the circumference of circle of radius r is
$C=2 \pi r$
Substituting the value of C,
$352=2 \times \frac{22}{7} \times r$
$352 \times 7=44 r$
$r=\frac{352 \times 7}{44}$
$r=56 \mathrm{~m}$
Thus, the radius of Circular Park is
.
Since, 7m wide road surrounds the circular park. Then
radius of outer circle $=$ radius of inner circle $+7$
$=56+7$
$=63 \mathrm{~m}$
Area of road = Area of outer circle-Area of inner circle
$=\frac{22}{7} \times 63 \times 63-\frac{22}{7} \times 56 \times 56$
$=12474-9856$
$=2618 \mathrm{~m}^{2}$