Question

The circumference of a circular garden is $572m$. Outside the garden a road,$3.5m$ wide, runs around it.Calculate the cost of repairing the road at the rate of $Rs.375per$ $100.sq.m$ ?

Answer 1

since the circumference of circular garden $=572m$

$\Rightarrow 2\pi r=572\Rightarrow 2.\frac{22}{7}.r=572\Rightarrow r=91m$

$\because r^{\prime }=r+3.5m\Rightarrow r^{\prime }=91+3.5\Rightarrow r^{\prime }=94.5m$

Hence, the area cover up by the road;

$=\pi {r^{\prime }}^2-\pi r^2=\frac{22}{7}({94.5}^2-{91}^2)=2040.5m^2$

given that the cost of reparing the road at the rate of $Rs375per100sq.m$

then the total cost for repairing the road

$=\frac{375}{100}\times 2040.5=Rs7651.88$