Question

The inner circumference of a circular track [given figure] is $220$ m. The track is $7$ cm wide everywhere . Calculate the cost putting up a fence along the outer circle at the rate of Rs.$2$ per meter.

Answer 1

Let the outer and inner radii of the track be $rm$ and $Rm$ respectively. Then,

Inner circumference $2\pi r=220m$

$\Rightarrow 2\times \frac{22}{7}\times r=220$ and $\Rightarrow r=2\frac{222\times 7}{2\times 22}=35m$

Since the track is $7m$ wide everywhere. Therefore,

$R=$ Outer radius $=r+7=(35+7)m=42m$

$\therefore$ Outer circumference $=2\pi R=2\times \frac{22}{7}\times 42m=264m$

Rate of fencing $=Rs.2$ per metre

$\therefore$ Total cost of fencing $=(Circumference\times rate)=Rs.(264\times 2)=Rs.528$