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An open box with a square base is to be ...

An open box with a square base is to be made out of a given quantity of cardboard of area `c^2` Show that the maximum volume of box is `c^3/[6sqrt3]`

Text Solution

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Let length, breadth and height =x,x,y respectively
According to question
`x^2+4xy=c^2`
`y=(c^2-x^2)/(4x)`
Volume of box=`x^2y`
`=x(c^2/x^2)/(4x)`
V(x)=`c^2/4x-x^3/4`
differentiate with respect to x
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