Q. volume, differentiation, etc (1 Viewer)

[marsenal]

An open tank is to be made of sheet iron; it must have a square base and sides perpendicular to the base. its capacity is to be 8m³.
Find, correct to the nearest centimetre, the side of the square base, and the depth, so that the least amount of sheet iron may be used.


I'm getting an answer for this, but I seem to be doing it in a really round about way, so I'm not confident that my answer is correct.

 

[BlackJack]

Hmm... how about this...

V = Ah = 8m³

But, A = b²

Therefore b²h = 8
h = 8 / b²

Now, SA = 4bh + b²
=32 / b + b²

dSA/db = 2b - 32 / b²

let it = 0 (prove it's a minimum, say end points zoom off into infnity)

Hence,
2b - 32 / b² = 0
2b³=32
b= 2 cuberoot(2), calculate value to centimetres.

 

[marsenal]

Cheers, that is the answer that I got so that's reassuring.