A cylindrical container with no top is to be constructed for a fixed amount of money. The cost of material for the bottom is 3 cents per square inch, and the cost of material for the lateral surface is 2 cents per square inch. Find the relationship between the radius and height of the container having the greatest volume.
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.
A cylindrical container with no top is to be constructed for a fixed amount of money. The cost of material for the bottom is 3 cents per square inch, and the cost of material for the lateral surface is 2 cents per square inch. Find the relationship between the radius and height of the container having the greatest volume.
Step by step
Solved in 4 steps
