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Question

Question 109

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. 11750, 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 = Rs. 5 per dm^2
Total cost of painting = Rs. 11750
Total surface area =Total cost of paintingCost of painting per dm2=117505
=2350 dm2
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 =2350dm2
94x2=2350x2=235094=25x=5
Hence, dimensions of the box are 5x×5=25dm,4x×5=20 dm and 3x×5=15 dm


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