Answer to Question #64604 in Calculus for Bryan

Question

19. A rectangular box has a square base with edge length x of at least 1 unit. The
total surface area of its six sides is 150 square units.
(a) Express the volume V of this box as a function of x.
(b) Find the domain of V (x).
(c) Find the dimensions of the box in part (a) with the greatest possible
volume. What is this greatest possible volume?

20. An open-top box is to have a square base and a volume of 13500 cm3. Find the dimensions of the box that minimize the amount of material used.

21. Find the dimension of the right circular cylinder of maximum volume that can
be inscribed in a right circular cone of radius R and height H.

22. A hollow plastic cylinder with a circular base and open top is to be made and
10 m2 plastic is available. Find the dimensions of the cylinder that give the
maximum volume and find the value of the maximum volume.