You are designing a 4 cm^3 right circular cylindrical can whose manufacture will take waste into account. There is no waste in cutting the aluminum for the side, but the top and bottom of radius r will be cut from squares that measure 4r units on a side. The total amount of aluminum used up by the can will therefore be A = 32r^2 + 2pi rh What is the ratio now of h to r for the most economical can? The ratio of h to r for the most economical can is ___? (type an exact answer in terms of pi as needed.)

You are designing a 4 cm^3 right circular cylindrical can whose manufacture will take waste into account. There is no waste in cutting the aluminum for the side, but the top and bottom of radius r will be cut from squares that measure 4r units on a side. The total amount of aluminum used up by the can will therefore be A = 32r^2 + 2pi rh What is the ratio now of h to r for the most economical can? The ratio of h to r for the most economical can is ___? (type an exact answer in terms of pi as needed.)

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter9: Surfaces And Solids

Section9.3: Cylinders And Cones

Problem 14E: A cylindrical orange juice container has metal bases of radius length 1 in. and a cardboard lateral...

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