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A cylindrical garden compost container with a circular base of diameter x and height y is to be made to contain 64π ft³ of soil. The container does not have a lid, that is, the container has an open top. What are the dimensions of the container that minimize the amount of material used to build the container ?

A cylindrical garden compost container with a circular base of diameter x and height y is to be made to contain 64π ft³ of soil. The container does not have a lid, that is, the container has an open top. What are the dimensions of the container that minimize the amount of material used to build the container ?

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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A cylindrical garden compost container with a circular base of diameter x and height y is to be made to contain 647 ft³ of soil. The container does not have a lid, that is, the container has an open top. What are the dimensions of the container that minimize the amount of material used to build the container ? Hint: The area of a circle of radius r is r². A cylinder (with bottom and top lid) with height h and radius r has volume Tr²h, and has surface area 2πrh+ 2πr².
Transcribed Image Text:A cylindrical garden compost container with a circular base of diameter x and height y is to be made to contain 647 ft³ of soil. The container does not have a lid, that is, the container has an open top. What are the dimensions of the container that minimize the amount of material used to build the container ? Hint: The area of a circle of radius r is r². A cylinder (with bottom and top lid) with height h and radius r has volume Tr²h, and has surface area 2πrh+ 2πr².
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