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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.
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Solution
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.
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