# Find the number of revolutions made

Question:

Find the number of revolutions made by a circular wheel of area 1.54 min rolling a distance of 176 m.

Solution:

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

Given that, $\quad$ area of circular wheel $=1.54 \mathrm{~m}^{2}$

$\Rightarrow \quad \pi r^{2}=1.54$ $\left[\because\right.$ area of circular $\left.=\pi r^{2}\right]$

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

$\therefore$ $r=0.7 \mathrm{~m}$

So, the radius of the wheel is $0.7 \mathrm{~m}$.

Distance travelled by a circlular wheel in one revolution = Circumference of circular wheel

$=2 \pi r$

$=2 \times \frac{22}{7} \times 0.7=\frac{22}{5}=4.4 \mathrm{~m} \quad[\because$ circumference of a circle $=2 \pi r]$

Since, distance travelled by a circular wheel $=176 \mathrm{~m}$

$\therefore \quad$ Number of revolutions $=\frac{\text { Total distance }}{\text { Distance in one revolution }}=\frac{176}{4.4}=40$

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