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

Can I assume that W = H = L

anonymous · Answer

dude....no its a square based prism.

anonymous · Answer

SA = 2 * b * sqrt(b^2+h^2/4) + b^2
V = 1/3 * b^2 * h

250 = 1/3 * b^2 * h
b = 5 * sqrt(30) / sqrt(h)

Substitute b into SA, calculate minimum of derivative in respect to h

anonymous · Answer

ok this is what we had so far...

S = 2x^2 + 250/x

after substituting for x, s==94.5 and x=4....

didnt seem right...

going to try your method now....assuming SA is surface area and b= ? sprt=?

anonymous · Answer

sqrt is square root
b is base length

anonymous · Answer

ok cool....

so then to find the smallest surface area, we substitute into b? (im not fantastic at maths) we have to make a graph and a table etc...

anonymous · Answer

you have b = 5 * sqrt(30) / sqrt(h)
so you substitute each b in SA to that, find derivative, and then the minimum

anonymous · Answer

ahhh ok........going to work on it right now

anonymous · Answer

soo whats the answer.....whats the smallest surface area in your workin out