Find the dimensions of the largest rectangular box with a square base and open top that can be made from 300cm^2 of metal.
2 answers
Any help would be great
if the box has dimensions x,x,h
x^2 + 4hx = 300
so, h = (300-x^2)/4x
by "largest" I assume you mean "having the largest volume".
v = x^2 * h = 4x(300-x^2) = 1200x - 4x^3
dv/dx = 1200 - 12x^2
max volume where 1200-x^2 = 0, or x = 10
So, the box is 10x10x5
x^2 + 4hx = 300
so, h = (300-x^2)/4x
by "largest" I assume you mean "having the largest volume".
v = x^2 * h = 4x(300-x^2) = 1200x - 4x^3
dv/dx = 1200 - 12x^2
max volume where 1200-x^2 = 0, or x = 10
So, the box is 10x10x5
2 answers