Mathematics
Mathematics
Problem
An open cylindrical vessel is to be made to hold 500 cm of liquid. The vessel has no lid. Which of the following values of the base radius (in cm) will minimise the amount of metal required? a) b) c) d)Intuitive explanation
This is an optimization problem where you need to minimize surface area subject to a volume constraint. Since the cylinder has no lid, the metal required is just the base plus the curved side—not a full closed surface. The key insight is to express the height in terms of the radius using the fixed volume, then write total surface area as a function of alone. Once you have a single-variable function, find its minimum using calculus by setting the derivative equal to zero.
Intuitive explanation
This is an optimization problem where you need to minimize surface area subject to a volume constraint. Since the cylinder has no lid, the metal required is just the base plus the curved side—not a full closed surface. The key insight is to express the height in terms of the radius using the fixed volume, then write total surface area as a function of alone. Once you have a single-variable function, find its minimum using calculus by setting the derivative equal to zero.