A cylindrical can with a closed top is to be constructed. Its bottom and top are to made of a material that costs $1 per square unit. Its side is to be made of a material that costs $4 per square unit. What is the radius of the bottom of the least expensive garbage can that can be constructed of volume 2 cubic units? It might be helpful to know that a cylinder of radius r and height h has side surface area of 2arh and volume of xr h. (Remember to test any critical number.)

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Cylinders

A cylinder is a three-dimensional solid shape with two parallel and congruent circular bases, joined by a curved surface at a fixed distance. A cylinder has an infinite curvilinear surface.

Cones

A cone is a three-dimensional solid shape having a flat base and a pointed edge at the top. The flat base of the cone tapers smoothly to form the pointed edge known as the apex. The flat base of the cone can either be circular or elliptical. A cone is drawn by joining the apex to all points on the base, using segments, lines, or half-lines, provided that the apex and the base both are in different planes.