Question

A road $3.5m$ wide surrounds a circular plot whose circumference is $44m.$ find the cost of paving the road at $Rs.50$ per $m^2.$

Answer 1

Let the ${}^{\prime }{r}^{\prime }$ and ${}^{\prime }{R}^{\prime }$ be the radii of the inner and outer circle respectively.
Circumference of the inner circle $=44m$
$2\pi r=44$

$2\times \frac{22}{7}\times r=44$

$r=\frac{44}{7}\times 44$

$r=7m$

So, the radius of the inner circle is $7m$
Width of the road $=3.5m$
So, radius of the outer circle $=7+3.5=10.5m$
Area of the road $=\pi R^2-\pi r^2$
$=\frac{22}{7}\times 10.5\times 10.5-\frac{22}{7}\times 7\times 7$
$=346.5-154=192.5$
Area of the road $=192.5m^2$
Cost of paving the road $=Rs.50$ per $m^2$
Total cost of paving the road $=192.5\times 50$
$=Rs.9625$