Question

A circular park of radius $20m$ has a road $5m$ wide running around it$.$ Find the cost of metalling the road at $₹14$ per square meter$.\left(Take\mathrm{\pi }=\frac{22}{7}\right)$

Answer 1

It is given that radius of a circular park$=20m$
Width of a road $=5m$
Inner radius of the park $r=20m$
Outer radius of the Park including the road $R=width+r$

$R=5+20$
$R=25m$
Area of the road $=\mathrm{\pi }\left({\mathrm{R}}^2-{\mathrm{r}}^2\right)$
$=\mathrm{\pi }\left(\mathrm{R}+\mathrm{r}\right)\left(\mathrm{R}-\mathrm{r}\right)$

$=\frac{22}{7}\left(25+20\right)\left(25-20\right)$
$=\frac{22}{7}\times 45\times 5$

The cost of metalling the road for $1$ square meter $=$$₹14$

The cost of metalling the road for $\frac{22}{7}\times 45\times 5$ square meter $=$$₹\frac{22}{7}\times 45\times 5\times 14$
$=$$22\times 45\times 5\times 2$

$=$$₹9900$
Hence, the cost of metalling the road at $₹14$ per square meter is $₹9900$