Question

External dimensions of a closed wooden box are in the ratio 5:4:3. If the cost of painting its outer surface at the rate of Rs 5 per dm² is Rs 11,750, find the dimensions of the box.

Answer 1

External dimensions of a closed wooden box are in the ratio 5:4:3.

Let the external dimensions of the closed wooden box be 5x, 4x and 3x.

The cost of painting = ₹ 5 per dm²

Total cost of painting = ₹ 11750

∴ Total surface area = `"Total cost of painting"/("Cost of painting per dm"^2) = 11750/5`

Total surface area of a cuboid = 2(lb + bh + hl)

= 2(5x × 4x + 4x × 3x + 3x × 5x)

= 2(20x² + 12x² + 15x²)

= 2 × 47x²

= 94x²

Since, total surface area = 2350 dm²

⇒ 94x² = 2350

⇒ `x^2 = 2350/94 = 25`

∴ x = 5

Hence, dimensions of the box are 5x × 5 = 25 dm, 4x × 5 = 20 dm and 3x × 5 = 15 dm.