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

Options

A. `40`
B. `30`
C. `10`
D. `48`

Answer

A

Explanation

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)`
`rArrpir^(2)=1.54` [`because` area of circular = `pir^(2)`]
`rArr r^(2)= (1.54)/(22)xx7rArrr^(2) = 0.49`
`:.r = 0.7m`
So, the radius of the wheel is `0.7m`.
Distance travelled by a circlular wheel in one revolution = Circumference of circular wheel
= `2pir`
= `2xx(22)/(7)xx0.7=(22)/(5)=4.4m` [`because` circumference of a circle = `2pir`]
Since, distance travelled by a circular wheel = 176m
`:.` 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.