Question

A roller is 4 m long and has a diameter of 0.7 m. It takes exactly 2000 rotations of the roller to level a road. If the cost of using the roller is Rs. 4 per square metres, then the total cost of levelling the road is : Assume, $\pi=\frac{22}{7} $

• A. Rs. 17600
• B. Rs. 35200
• C. Rs. 70400
• D. Rs. 140800

Answer 1

The Correct Option is C

To calculate the total cost of leveling the road with the roller, we need to first determine the area covered by one rotation of the roller and then use this information to calculate the total area covered and its cost. 

1. The roller is in the shape of a cylinder. The surface area of the side of a cylinder is calculated using the formula: \(A = \text{Circumference} \times \text{Length}\).
2. The circumference of the circle (which is the base of the cylinder) is given by: \(C = \pi \times \text{Diameter}\).
3. Substituting the provided values: \(C = \frac{22}{7} \times 0.7 = 2.2\) meters.
4. Thus, the area covered by one complete rotation of the roller is: \(A = 2.2 \times 4 = 8.8\) square meters.
5. Since the roller takes exactly 2000 rotations to level the road, the total area covered is: \(2000 \times 8.8 = 17600\) square meters.
6. The cost of leveling 1 square meter is Rs. 4. Therefore, the total cost of leveling the entire road is: \(17600 \times 4 = 70400\) rupees.

Therefore, the total cost of leveling the road is Rs. 70400.