A metal storage tank with fixed volume V0 = 360π m^3 is to be constructed in the shape of a right circular cylinder (including the bottom) surmounted by a hemisphere. A picture is given below. What dimensions will require the least amount of metal? Show and organize your work; use the first derivative test or the second derivative test or other tools to check that yours is the desired optimal solution.

A metal storage tank with fixed volume V0 = 360π m^3 is to be constructed in the shape of a right circular cylinder (including the bottom) surmounted by a hemisphere. A picture is given below. What dimensions will require the least amount of metal? Show and organize your work; use the first derivative test or the second derivative test or other tools to check that yours is the desired optimal solution.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 94E

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Question

A metal storage tank with fixed volume V0 = 360π m^3
is to be constructed in the shape of a right circular cylinder (including the bottom) surmounted by a hemisphere. A picture is given below.
What dimensions will require the least amount of metal? Show and organize your work; use the first
derivative test or the second derivative test or other tools to check that yours is the desired optimal
solution.

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