6.2 - 2015 Q9
A solid glass cylinder, which is used in an expensive laser amplifier, has a volume of 75 π cm3.
The cost of polishing the surface area of this glass cylinder is £2 per cm2 for the curved surface area and £3 per cm2 for the circular top and base areas.
Given that the radius of the cylinder is r cm,
(a) show that the cost of the polishing, £C, is given by: (4)
The cost of polishing the surface area of this glass cylinder is £2 per cm2 for the curved surface area and £3 per cm2 for the circular top and base areas.
Given that the radius of the cylinder is r cm,
(a) show that the cost of the polishing, £C, is given by: (4)
(b) Use calculus to find the minimum cost of the polishing, giving your answer to the nearest pound.(5)
(c) Justify that the answer that you have obtained in part (b) is a minimum.(1)
(c) Justify that the answer that you have obtained in part (b) is a minimum.(1)