# Lagrange multipliers

A hot water tank is a vertical cylinder surmounted by a hemispherical top of the same diameter . The tank is designed to hold 750m^3 of liquid.

Determine using Lagrange multipliers the total height and the diameter of the tank if surface heat loss is to be a minimum.

© BrainMass Inc. brainmass.com October 10, 2019, 12:26 am ad1c9bdddfhttps://brainmass.com/math/geometry-and-topology/lagrange-multipliers-hemispherical-top-291824

#### Solution Preview

Hello and thank you for posting your question to Brainmass!

The solution is attached below in two files. the files are identical in content, only differ in format. The first is in MS Word format, while the other is in Adobe pdf format. Therefore you can choose the format that is most suitable to you.

Let r be the tank's radius and h the cylinder's height.

The volume ...

#### Solution Summary

Lagrange multipliers are employed.

$2.19