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A box is constant volume c is be twice as long as it is wide. The material on the top and four sides cost three times as much per square meter as that in the bottom, then the most economic dimensions are ____

Class: 9

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Detailed Solution

Let length be l
Breadth be b
Height be h
l = 2b
volume of box = c
c = 2b2h
area of %b = 2b2
Area of sides = 2bh + 2bh + bh + bh
= 6bh
Let r be cost for bottom and for to p and side cost be 3r
f = r(2b2) + 3r(2b2 + 6bh)
r(8b2 + 18bh)
c = 2b2h

16b3 = 9c

Hence volume will be minimum when
Question Image

Hence

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