A closed wood storage having a volume of 27 in.3 is to be in the form of a right-circular cylinder. The circular top and bottom are cut from square pieces of wood. Using calculus, find the radius and height of the wood storage if the least amount of wood is to be used in its manufacture. Include the wood that is wasted when obtaining the top and bottom. (Volume of a cylinder is r²h, where r is the radius and h is the height.)

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
Section9.1: Prisms, Area And Volume
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A closed wood storage having a volume of 27 in.³ is to be in the form of a
right-circular cylinder. The circular top and bottom are cut from square pieces of
wood. Using calculus, find the radius and height of the wood storage if the least
amount of wood is to be used in its manufacture. Include the wood that is wasted
when obtaining the top and bottom. (Volume of a cylinder is r²h, where r is the
radius and h is the height.)
Transcribed Image Text:A closed wood storage having a volume of 27 in.³ is to be in the form of a right-circular cylinder. The circular top and bottom are cut from square pieces of wood. Using calculus, find the radius and height of the wood storage if the least amount of wood is to be used in its manufacture. Include the wood that is wasted when obtaining the top and bottom. (Volume of a cylinder is r²h, where r is the radius and h is the height.)
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