We have a piece of cardboard that is 50 cm by 20 cm and we are going to cut out the corners and fold up the sides to form a box. Please determine the height of the box that will give a maximum volume.

A cylindrical container has a volume of 84 cubic inches and a radius of 3 inches. Find the height of the container.

If the radius length of one sphere is three times as long as the radius length of another sphere, how do the surface areas of the spheres compare? How do the volume compare?

Zaidah plans a raised flower bed 2 ft high by 12 ft wide by 15 ft long. The mulch, soil, and peat mixture used to fill the raised bed costs 15.75 per cubic yard. What is the total cost of the ingredients used to fill the raised garden?