Question

A road which is $7m$ wide surrounds a circular park whose circumference is $352m$. The area of the road is

• A. $2618m^2$
• B. $2624m^2$
• C. $2630m^2$
• D. $2724m^2$

Answer 1

The correct option is A $2618m^2$

.The circumference of the circular park is 352 m.

$C=2\pi r$

$352=2\times \frac{22}{7}\times r$

$r=\frac{352\times 7}{2\times 22}$

$r=56m$

The radius of the bigger circle is,

$R=56+7=63m$

The area of the road is the difference between the area of bigger circle and the area of the smaller circle.

$A=\pi R^2-\pi r^2$

$=\pi \left(R^2-r^2\right)$

$=\frac{22}{7}\left({\left(63\right)}^2-{\left(56\right)}^2\right)$

$=\frac{22}{7}\left(3969-3136\right)$

$=\frac{22}{7}\times 833$

$=2618m^2$

The area of the road is $2618m^2$