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 Breadth + Length Height + Breadth Height )
So,
Total surface area of cuboid = 2 ( 5 x 4 x + 5 x 3 x + 4 x 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 )
Hope this information will clear your doubts about Mensuration.
If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.
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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 Breadth + Length Height + Breadth Height )
So,
Total surface area of cuboid = 2 ( 5 x 4 x + 5 x 3 x + 4 x 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 )
Hope this information will clear your doubts about Mensuration.
If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.
Regards