Question

The volume of an open box with a square base is 4,000 cu.cm.. Find the dimensions of the box if the material used to make the box is minimun. (Solution musy be with Differential Calculus)

Answer 1

Recall that the perimeter of a cube :
A = l^2 + 4lh but because it is an open box than we will say l = side length

V=l^2h

so 4000 cm ^3 =l^2h

so solve for l

\[l = \sqrt{\frac{ 4000 }{ h }}\]

Substitute that back into the Area formula.

\[A =(\sqrt{\frac{ 4000 }{ h }})^{2} h\]

simplify this and take the derivate. Make it = to zero and solve for h. The solve backwards...I think..

Answer 2

In the last formula, is it "squared"? or "cube"?

Answer 3

The volume formula is length squared times height.