Question

# The radius of a wheel is 0.25m. Find the number of revolutions it will make to travel a distance of 11kms.

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Hint: To solve this question we find the distance covered by the wheel in 1 revolution. Then we find the number of revolutions made for 11kms using direct proportion property. $\left( {{{\text{x}}_1}{{\text{y}}_2} = {{\text{x}}_2}{{\text{y}}_1}} \right)$.

Given Data: Radius of the wheel (r) = 0.25m
Distance covered in 1 revolution = Circumference of the wheel
= 2πr
= 2 × $\dfrac{{22}}{7}$ × 0.25
= $\dfrac{{11}}{7}$m.
Given total distance = 11km = 11000m.
The number of revolutions and the distance covered are in direct proportion. (I.e. if one value increases the other value increases).
(Total distance = total number of revolutions × distance covered in 1 revolution)
Then the number of revolutions = 11000 × $\dfrac{7}{{11}}$
= $\dfrac{{77000}}{{11}}$
= 7000.
Therefore the number of revolutions = 7000.

Note: In such types of problems it is important to identify if the variables are either in direct proportion or indirect proportion and then apply the respective formula.
The variables are in direct proportion if one decreases/ increases with the decrease/increase in the other respectively.
The variables are in inverse proportion if one increases/decreases with the decrease/increase in the other respectively.