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A plastic drinking cup is cylindrical in shape, with an open top. It is required to hold 300 cm³ of fluid when filled to the top. The company making the cups aims to improve its profits by minimising the amount of plastic it uses in each cup, which is proportional to the surface area. Find the values of the radius, r, and height, h, which minimise the surface area and hence the cost of production.

A plastic drinking cup is cylindrical in shape, with an open top. It is required to hold 300 cm³ of fluid when filled to the top. The company making the cups aims to improve its profits by minimising the amount of plastic it uses in each cup, which is proportional to the surface area. Find the values of the radius, r, and height, h, which minimise the surface area and hence the cost of production.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(c) A plastic drinking cup is cylindrical in shape, with an open top. It is required to hold 300 cm³ of fluid when filled to the top. The company making the cups aims to improve its profits by minimising the amount of plastic it uses in each cup, which is proportional to the surface area. Find the values of the radius, r, and height, h, which minimise the surface area and hence the cost of production.
Transcribed Image Text:(c) A plastic drinking cup is cylindrical in shape, with an open top. It is required to hold 300 cm³ of fluid when filled to the top. The company making the cups aims to improve its profits by minimising the amount of plastic it uses in each cup, which is proportional to the surface area. Find the values of the radius, r, and height, h, which minimise the surface area and hence the cost of production.
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