A conical container is made by cutting a sector with the center angle of alpha from a round sheet iron with radius R. the volume of the container is the largest when the center angle of the sector is larger

A conical container is made by cutting a sector with the center angle of alpha from a round sheet iron with radius R. the volume of the container is the largest when the center angle of the sector is larger

Let R be the bottom radius and H be the height of a conical vessel, then 2 π r = α R, & nbsp; & nbsp; r = α R / (2 π). & nbsp; H = √ (R & amp; sup2; - R & amp; sup2;) and R be the independent variable. The volume of the vessel v = (1 / 3) π R & amp; sup2; H = (1 / 3) π R & amp; sup2; √ (R & amp; sup2; - R & amp; sup2;)