A grain silo consists of a right circular cylinder of radius feet surmounted by a…
MATHEMATICS · Single correct · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives
Problem
A grain silo consists of a right circular cylinder of radius r feet surmounted by a hemispherical roof of the same radius. The silo must enclose exactly 3000 ft3 of volume. Ignoring any internal supports, the exterior surface includes the curved cylindrical wall, the hemispherical roof, and a flat circular floor. Which of the following relationships between the cylinder’s height h and the radius r minimizes the amount of material required to build the silo?
(a) h=2r
(b) h=r
(c) h=21r
(d) h=23r