Homework Help is Here – Start Your Trial Now!
Math
Calculus
Let r and h be the radius and height of the cylinder respectively. Then its surface area is S(r, h) = 3ñr² +2Ãrh, and volume is V(r, h) = ár²h + ¾ör³. Setting up and solving the equation VV = XVS, we will get r = h.

Let r and h be the radius and height of the cylinder respectively. Then its surface area is S(r, h) = 3ñr² +2Ãrh, and volume is V(r, h) = ár²h + ¾ör³. Setting up and solving the equation VV = XVS, we will get r = h.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
See similar textbooks
icon
Related questions
Question

the second pic is from the answer key, so the answers should match

7. Let r and h be the radius and height of the cylinder respectively. Then its surface area is S(r, h) = 3ær² + 2ärh, and volume is V(r, h) = πr²h + ¾ár³. Setting up and solving the equation VV = XVS, we will get r = = h.
Transcribed Image Text:7. Let r and h be the radius and height of the cylinder respectively. Then its surface area is S(r, h) = 3ær² + 2ärh, and volume is V(r, h) = πr²h + ¾ár³. Setting up and solving the equation VV = XVS, we will get r = = h.
7. A grain silo is to be built by attaching a hemispherical roof and a flat floor onto a circular cylinder. Use Lagrange multipliers to show that for a total surface area S, the volume of the silo is maximized when the radius and height of the cylinder are equal.
Transcribed Image Text:7. A grain silo is to be built by attaching a hemispherical roof and a flat floor onto a circular cylinder. Use Lagrange multipliers to show that for a total surface area S, the volume of the silo is maximized when the radius and height of the cylinder are equal.
Expert Solution
steps

Step by step

Solved in 3 steps with 8 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS