Answered: A box with a square base with side…

A box with a square base with side length b and height h and with an open-top must have a volume of 500 cm 3 . Find the dimensions of the box ( b and h ) that minimize the amount of material used.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter8: Further Techniques And Applications Of Integration

Section8.3: Volume And Average Value

Problem 17E

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Question

A box with a square base with side length b and height h and with an open-top must have a volume of 500 cm 3 . Find the dimensions of the box ( b and h ) that minimize the amount of material used.
Find the volume of the solid obtained by rotating the region bounded by the curves y = sin x and y = cos x, 0 ≤ x ≤ π 4 about the line y = − 1