LIL BROS MATHS: I NEED HELP. Use algebra to determine the dimensions of a spare based popper box that will hold 250ml, yet has the smallest possible surface area. Use a graphics calculator and show all working out........anyone know how to do this properly? There are lots of answers.....and no google help..

Question

anonymous · Answer

I am going to try to solve this by hand.

anonymous · Answer

haha ok....i need epic help. :-(

anonymous · Answer

square box of vol 250 ml
minimize: smallest possible surface area
requires light algebra
will attempt in morning if no one gets back to you

anonymous · Answer

If the box is square shaped, all its sides are the same length. So length=width=height

volume=length x width x height.

250=x^3

x=6.30=length=width=height.

anonymous · Answer

unless i interpreted this question incorrectly and "spare based popper box" does not refer to a cube.

anonymous · Answer

the box isn't square shaped,it's a rectangular prism (base is square+top,but 4 faces are rectangular)

anonymous · Answer

OK
$$V =250=x ^{2}y$$$$y =250/x ^{2}$$$$SA =2xy+2xy+2x ^{2}=4xy+2x ^{2}$$Find derivative of SA. Minimise