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 $d m^{2}$ 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 $= \frac{T o t a l c o s t o f p a i n t i n g}{C o s t o f p a i n t i n g p e r d m^{2}} = \frac{11750}{5}$
$= 2350 d m^{2}$
Total surface area of a cuboid
$= 2 (l b + b h + h l) = 2 (5 x \times 4 x + 4 x \times 3 x + 3 x \times 5 x) = 2 (20 x^{2} + 12 x^{2} + 15 x^{2}) = 2 \times 47 x^{2} = 94 x^{2}$
Since, total surface area $= 2350 d m^{2}$
$\Rightarrow 94 x^{2} = 2350 \Rightarrow x^{2} = \frac{2350}{94} = 25 ∴ x = 5$
Hence, dimensions of the box are $5 x \times 5 = 25 d m, 4 x \times 5 = 20 d m$ and $3 x \times 5 = 15 d m$

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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.

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 $d m^{2}$ is Rs. 11750, find the dimensions of the box.