Question

Question 18
Find the number of revolutions made by a circular wheel of area $1.54m^2$ in rolling a distance of 176 m.

Answer 1

Let the number of revolutions made by a circular wheel be n and the radius of circular wheel be r.

Given that, area of circular wheel $=1.54m^2$

$\Rightarrow \pi r^2=1.54[\because areaofcircular=\pi r^2]$

$\Rightarrow r^2=\frac{1.54}{22}\times 7\Rightarrow r^2=0.49$

$r=0.7m$

So, the radius of the wheel is 0.7 m.

Distance travelled by a circular wheel in one revolution

= Circumference of circular wheel

$=2\pi r$

$=2\times \frac{22}{7}\times 0.7$

$=\frac{22}{5}=4.4m[\because circumferenceofacircle=2\pi r]$

Since, distance travelled by a circular wheel = 176 m

$\therefore Numberofrevolutions$

$=\frac{Totaldistance}{Distanceinonerevolution}=\frac{176}{4.4}=40$

Hence, the required number of revolutions made by a circular wheel is 40.