Question

A road roller takes 750 complete revolutions to move once over to level a road. Find the area of road if the diameter of a road roller is 84 cm and length is 1m.

Answer 1

Hint: In one revolution, the road roller will cover an area equal to its lateral surface area. First work out on the radius of the roller. Second work out on the area of the road by using the formula $\left( A=750\times \text{Area covered in one revolution} \right)$.

Complete step-by-step answer:
 Given that,
Length of roller = h = 1m
Diameter of the roller = 84 cm
Therefore, Radius of the roller = $r=\dfrac{84}{2}=42$ cm
 Radius of the roller = $\dfrac{42}{100}$ m
Also, given that the roller takes 750 complete revolutions to level the whole road.
Therefore, the area of road = 750 (Area covered in one revolution)
The area of road = 750 (Lateral surface area of cylinder)
The area of road = $750\times 2\pi rh$
The area of road = $750\times 2\times \dfrac{22}{7}\times \dfrac{42}{100}\times 1=750\times 2\times 22\times \dfrac{6}{100}$
The area of road = $\dfrac{1500\times 132}{100}=15\times 132=1980$
Hence, the area of the road is 1980${{m}^{2}}$.

Note: Alternatively, the question is solved as follows
Length of roller = 1m = 100 cm
Circumference of roller = $\pi D=\dfrac{22}{7}\times 84=264$cm
Length of road =$264\times 750=198000$cm
Width of road = length of roller = 100 cm
Area of road = $198000\times 100=19800000\text{ c}{{\text{m}}^{2}}$ or 1980${{m}^{2}}$