Homework SourseA box with a square base and no top is to have a volume of 3
A box with a square base and no top is to have a volume of 32 cubic inches. What dimensions give the least possible surface outside area. (Ignore the thickness of the material.)
Solution
S.A=4ah+a^2 V=a^2*h=32 h=32/a^2 SA=128/a+a^2 for minimising dSA/da=0 =-128/a^2 + 2a=0 a^3=64 a=(64)^1/3 h=32/(64)^2/3
