14. A box has a square base of side x and height y. (a) Find the dimensions x, y for which the volume is 12 and the surface area is as small as possible. (b) Find the dimensions for which the surface area is 20 and the volume is as large as possible. Hint: (a) The volume V = x²y = 12. Minimize the surface area A = 2x2 + 4xy.
14. A box has a square base of side x and height y. (a) Find the dimensions x, y for which the volume is 12 and the surface area is as small as possible. (b) Find the dimensions for which the surface area is 20 and the volume is as large as possible. Hint: (a) The volume V = x²y = 12. Minimize the surface area A = 2x2 + 4xy.
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 40E: For a right circular cone, the dimensions are r=6 cm and h=8 cm. If the length of the radius is...
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Transcribed Image Text:14. A box has a square base of side x and height y.
(a) Find the dimensions x, y for which the volume is 12 and the surface area is as small as
possible.
(b) Find the dimensions for which the surface area is 20 and the volume is as large as possible.
Hint: (a) The volume V = x²y = 12. Minimize the surface area A = 2x2 + 4xy.
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