I know i should be able to find my mistake but i am missing something.
11. An open rectangular box is to be made with a square base, and its capacity is to be 4000 cm3. Find the length of the side of the base when the amount of material used to make the box is as small as possible. (ignore ‘flaps’).
V = l ^2 * h
SA = l^2 + 4lh
h = 4000 / l^2
SA = l^2 + 16000 l^(-1)
Derive SA = 2l - 16000 l^(-2)
set derive of SA = 0, solve for l
i get l = the cube root of 16000 = approx 25.19...
but i've been told the answer is 20. Where is my mistake?
Muchos Gracias
11. An open rectangular box is to be made with a square base, and its capacity is to be 4000 cm3. Find the length of the side of the base when the amount of material used to make the box is as small as possible. (ignore ‘flaps’).
V = l ^2 * h
SA = l^2 + 4lh
h = 4000 / l^2
SA = l^2 + 16000 l^(-1)
Derive SA = 2l - 16000 l^(-2)
set derive of SA = 0, solve for l
i get l = the cube root of 16000 = approx 25.19...
but i've been told the answer is 20. Where is my mistake?
Muchos Gracias
