Question

The outer rolling surfaces of 8 similar small rollers, each having a radius of 9 cm and length as 12 cm are to be painted at a rate of Rs. 15 / \( \text{cm}^2 \). What will be the total cost of painting (in Rs.)?

• A. 80788.7
• B. 80488.7
• C. 81280.5
• D. 81388.8

Hint:

In mensuration, "rolling surface" always refers to the curved part, excluding the circular flat ends.

Answer 1

The Correct Option is D

Concept: The "rolling surface" of a cylinder (roller) is its Curved Surface Area (CSA). \[ \text{CSA} = 2\pi rh \] Where \(r\) is radius and \(h\) is length (height).
Step 1: Calculate the CSA of one roller.
\(r = 9 \text{ cm}\), \(h = 12 \text{ cm}\), \(\pi \approx 3.14159\). \[ \text{CSA} = 2 \times 3.14159 \times 9 \times 12 = 678.24 \text{ cm}^2 (\text{approx}) \]

Step 2: Calculate total area for 8 rollers and the total cost.
Total Area = \(8 \times 678.24 = 5425.92 \text{ cm}^2\).
Total Cost = \(5425.92 \times 15 = 81388.8\).