Answer to Question #178457 in Calculus for Max

Question

A box with a square base and with height f(x) is to be constructed so that it has a volume of 1000 cubic centimeters. What are the possible dimensions of the box?

Thank you so much!

Answer 1

Let $x\ cm=$ the side of the base, $x>0.$ If the height of a box is $f(x),$ then

$$x^2f(x)=1000$$

$$f(x)=\dfrac{1000}{x^2}, x>0$$