external dimensions of a closed wooden box in the ratio 5 : 4 : 3 . if the cost of painting its outer surface at the rate of Rs 5 per m² is Rs 11,750. find the dimensions of the box .

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Please find below the solution to the asked query:

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

Let ratio coefficient =  x  , So 

Length of closed wooden box  = 5 x  , Breadth of closed wooden box  = 4 x  and Height of closed wooden box  = 3 x 

We know total surface area of cuboid  =  2 ( Length $\times$ Breadth + Length $\times$ Height +  Breadth $\times$ Height )

So,

Total surface area of cuboid =  2 ( 5 x  $\times$ 4 x  + 5 x  $\times$ 3 x  + 4 x  $\times$ 3 x ) = 2 ( 20 x² + 15 x² + 12 x² ) = 2 ( 47 x² ) = 94x²

And

If the cost of painting its outer surface at the rate of Rs 5 per m² is Rs 11,750. So


5 ( 94 x² ) =  11750

470 x ² =  11750

x ² = 25

x  = 5

Therefore,

Dimensions of the box : Length of closed wooden box  = 5( 5 ) = 25 m, Breadth of closed wooden box  = 4( 5 ) = 20 m and Height of closed wooden box  = 3( 5 ) = 15 m                                                ( Ans )


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