Find the number of revolutions made by a circular wheel of area 1.54 m^{2} in 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, area of circular wheel = 1.54 m^{2}

⇒ `pir^2 = 1.54` .....[∵ Area of circular πr^{2}]

⇒ `r^2 = 1.54/22 xx 7`

⇒ `r^2 = 0.49`

∴ r = 0.7 m

So, the radius of the wheel is 0.7 m

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

= `2 pir`

= `2 xx 22/7 xx 0.7`

= `22/5`

= 4.4 m ......[∵ Circumference of a circle = 2πr]

Since, distance travelled by a circular wheel = 176 m

∴ Number of revolutions = `"Total distance"/"Distance in one revolution"`

= `176/4.4`

= 40

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