Multivariable Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 0-53849-787-4
ISBN 13: 978-0-53849-787-9

Chapter 14 - Partial Derivatives - 14.7 Exercises - Page 979: 46

Answer

Dimensions of a box with volume 1000 and minimal surface area must be $a=b=c=10 cm$

Work Step by Step

Volume of a box is given by $V=abc=1000 cm^3$ Surface area, $S=2ab+2bc+2ca$ This implies $\nabla V=\lt ab,bc,ca \gt$ and $\nabla S=\lt 2b+2c,2c+2a,2a+2b \gt $ After solving we get, $a=b=c=10 cm$ Hence, the dimensions of a box with volume 1000 and minimal surface area must be $a=b=c=10 cm$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.