Question

The outer edge of a circular running track is $440$ m long. If it is widened by $5$ m all around, find the cost of widening it at the rate of Rs. $8$ per m ?

Answer 1

Perimeter of track $=2\pi r$

$2\pi r=440m$

$u=\frac{440\times 7}{44}=76m$

Radius of road$=70+5=75$m

Area of road $=\pi r^2$

$=\frac{22}{7}\times 75\times 75$

$=17678.57m^2$

Area of track$=\pi r^2=\frac{22}{7}\times 70\times 70m^2$

$=220\times 70m^2=15400m^2$

Area of widening road$=$ Area of road $-$ Area of track

$=17678.57-15400$

$=2278.57m^2$

$1m^2$ costs $=$Rs. $8/-$

$2278.57$ costs $=$Rs. $8\times 2278.57$/-

$=$Rs. $18228.56$.