Question

The diameter of a circular park is $74m.$ A uniform path $3m$ wide runs around outside$.$ Find the cost of levelling the path at $₹15.50$ per square meter$.$

Answer 1

It is given that diameter of a circular park $=$$74m.$

Radius $r=\frac{74}{2}$

$r=37m$

Width of the path $=$$3m$

Inner radius of the park $r=37m$
Outer radius of the Park including the road $R=width+r$

$R=3+37$
$R=40m$
Area of the road $=\mathrm{\pi }\left({\mathrm{R}}^2-{\mathrm{r}}^2\right)$
$=\mathrm{\pi }\left(\mathrm{R}+\mathrm{r}\right)\left(\mathrm{R}-\mathrm{r}\right)$

$=\frac{22}{7}\left(40+37\right)\left(40-37\right)$
$=\frac{22}{7}\times 77\times 3$

$=22\times 11\times 3$
$=726m^2$
Hence, the Area of the road is $726m^2$