Question

Find the number of revolutions made by a circular wheel of area $1.54m^2$ in rolling a distance of $176m$.

Answer 1

Distance covered by wheel in n revolutions with radius $r=2\pi rn.$

$\therefore 2\pi rn=176m$.........(i)

Area of wheel (circular)= $1.54m^2$

$\Rightarrow \pi r^2=1.54$

$\Rightarrow r^2=\frac{1.54}{\pi }=\frac{154\times 7}{22\times 100}=\frac{7\times 7}{10\times 10}$

$\Rightarrow r=0.7m$

Now, $2\pi rn=176$

$\Rightarrow 2\times \frac{22}{7}\times 0.7\times n=176$ [From (I)]

$\Rightarrow n=\frac{176\times 7\times 10}{2\times 22\times 7}=40$

Hence , $n=40$ revolutions.