# A road which is 7 m wide surrounds a circular park whose circumference is 352 m.

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

$=\frac{22}{7} \times 63 \times 63-\frac{22}{7} \times 56 \times 56$

$=12474-9856$

$=2618 \mathrm{~m}^{2}$