I am having trouble understanding the solution Greg provided for this.
Can we generalize that the max volume can be obtained by taking the 2 least quantities i.e. 10 & 8 in this case?
Try fitting the cylinder in the cube. How do you think it is going to look like?
It will fit in a cube of side 12 or 10 or 8.
Right?
Well, yes. But we don’t have a cube.
Hey, what you would want to do here is first of all try to understand which is the maximum base possible for the cylinder, the base circumference needs to fit in a rectangle that’s 12x10, which means that the maximum diameter possible for the base circumference of the cylinder will be 10, otherwise it won’t fit in the rectangle. As far as the height is concerned you can just take the maximum height possible which is 8. If you put these numbers in the formula you’ll get 628