What's the reason for differentiating?

[Thepiman12]

Homework Statement

A closed cylinder is required to have a volume of 40m^3 but made with the minimum amount of material. Determine the radius and height the cylinder must have to meet such a requirement.

V= πr^2h

Steps needed:

a) Insert value and transpose for h
b) Then sub into the area formula
c) Then differentiate

Homework Equations

V= πr^2h

The Attempt at a Solution

V= πr^2h
40= πr^2h
40/h= πr^2
h=πr^2/40

A= 2πrh+2πr^2 Subbing in h= πr^2/40
A= 2πr(πr^2/40)+2πr^2

 

[SammyS]

Homework Statement

A closed cylinder is required to have a volume of 40m^3 but made with the minimum amount of material. Determine the radius and height the cylinder must have to meet such a requirement.

V= πr^2h

Steps needed:

a) Insert value and transpose for h
b) Then sub into the area formula
c) Then differentiate

Homework Equations

V= πr^2h

The Attempt at a Solution

V= πr^2h
40= πr^2h
40/h= πr^2
h=πr^2/40

A= 2πrh+2πr^2 Subbing in h= πr^2/40
A= 2πr(πr^2/40)+2πr^2

What's your question?


Now you need to do step c.

c) Then differentiate.​

Then a little bit more.

 

[Thepiman12]

I expanded the brackets and got 2πr^2+80r^-1

And differentiated that to 4πr-80r^-2 Is that correct?

After that how would I go on to find the radius r?

 

[SammyS]

I expanded the brackets and got 2πr^2+80r^-1

And differentiated that to 4πr-80r^-2 Is that correct?

After that how would I go on to find the radius r?

The answer to that is related to "What is the reason for differentiating?" .

When you solved

V = 2πr²h

for h, you made a mistake.

What you have is actually 1/h .