A closed cylindrical can is to be manufactured so that its volume is
MATHEMATICS · Multi-part · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
A closed cylindrical can is to be manufactured so that its volume is 500cm3. The material for the curved surface costs Rs. 2 per square centimetre, while the material for the top and bottom costs Rs. 3 per square centimetre.
(i) Express the total manufacturing cost C(r) as a function of the radius r of the base of the can.
(ii) Find the radius and the height of the can that minimise the total cost.
(iii) Show that the critical point obtained in part (ii) indeed gives a minimum cost and calculate this minimum cost to the nearest paisa.