Question

A wooden box (open at the top) of thickness 0.5 cm, length 21 cm, width 11 cm, and height 6 cm is painted on the inside. The expenses of painting are Rs. 70. What is the rate of painting per square centimetre?

• A. Rs. 0.7
• B. Rs. 0.5
• C. Rs. 0.1
• D. Rs. 0.2

Hint:

For an open box, calculate the area of the sides and bottom, and divide the total cost by the area to get the rate per square centimetre.

Answer 1

The Correct Option is A

The box is open at the top, so we need to calculate the surface area of the sides and the bottom. The dimensions of the box are: - Length \( l = 21 \, \text{cm} \) - Width \( w = 11 \, \text{cm} \) - Height \( h = 6 \, \text{cm} \) The surface area of the box consists of: - 2 sides of length \( 21 \times 6 \) - 2 sides of width \( 11 \times 6 \) - The bottom area \( 21 \times 11 \) The total surface area is: \[ \text{Surface area} = 2 \times (21 \times 6) + 2 \times (11 \times 6) + (21 \times 11) \] \[ = 2 \times 126 + 2 \times 66 + 231 \] \[ = 252 + 132 + 231 = 615 \, \text{cm}^2 \] The total cost of painting is Rs. 70. The rate of painting per square centimetre is: \[ \text{Rate} = \frac{70}{615} \approx 0.7 \, \text{Rs. per cm}^2 \] Thus, the answer is a. Rs. 0.7.