A cylindrical container with a closed bottom and a removable lid must hold exactly of…
MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives
Problem
A cylindrical container with a closed bottom and a removable lid must hold exactly 1000cm3 of liquid. The lateral surface of the cylinder is made from material costing 0.02 dollars per square centimetre, while the top and bottom are made from stronger material costing 0.05 dollars per square centimetre. Let the radius of the base be r centimetres and the height be h centimetres.
(a) Write formulas for the total material cost C and volume V in terms of r and h.
(b) Use the volume requirement to express C as a function of one variable.
(c) Determine the critical point of the cost function and the corresponding values of r and h, to two decimal places.
(d) Justify that the critical point in part (c) gives the minimum possible material cost.
(e) Calculate the minimum material cost in dollars.