Don't ask Just make it

Calculus Level 4

A box of maximum volume with top open is to be made by cutting out four equal squares from four corners of a square Aluminium sheet and then folding up the flaps. The square aluminium sheet has the side length $X$ .

If the side length of the square cut-off can be represented as $\frac{97X}{n}$ , find $n$ .

The answer is 582.

1 solution

Harsh Poonia
Feb 17, 2019

Volume of the box so formed is $y\cdot(x-2y)^2=V$ .
As $V$ is a function of $y$ , we can set its derivative equal to zero for the maxima. $\frac {dV}{dy}=0 \implies (x-2y)^2\cdot1+y\cdot2\cdot(x-2y)\cdot(-2)=0 \text{ (Using Product Rule)}\implies x=6y$ Now $y= x/6=97x/n.$ Solving yields $n=97\times6=\boxed{582}$

Don't ask Just make it

The answer is 582.

1 solution

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