Question

A right circular cylinder is such that the sum of the height and the circumference around the base is 30 cm. What is the radius that produces a maximum volume?

Answer 1

@ganeshie8

Answer 2

I believe this is optimization

Answer 3

\[h+2 \pi r =30\]

Answer 4

I am not sure if I can make this statement
appreciate any help @zepdrix

Answer 5

\[V=\pi r^2 h\]

Answer 6

I wanted to use the first statement into the second statement, but not sure I am doing this correct. I know the final answer but I am trying to figure out the process

Answer 7

Mmmm I think you're on the right track.\[\Large\rm V(r)=\pi r^2 (h)\]\[\Large\rm V(r)=\pi r^2 (30-2\pi r)\]\[\Large\rm V(r)=30\pi r^2-2\pi^2 r^3\]And then we want to differentiate with respect to...... r I guess?

Answer 8

And then set our Volume derivative equal to zero.
And look for r values that correspond to critical points of the volume function.

Answer 9

ok here is a really dumb question on my part, when I take the derivative of the first term do I end up with 60 (pi)^2 r?

Answer 10

pi is a constant and I am starting to confuse myself

Answer 11

hehe

Answer 12

or is it 60 pi r?

Answer 13

glad you find this funny.........I have been going cross eye trying to do this problem

Answer 14

(30pi) r^2 turns into 2(30pi) r or 60pi r

yah the second one.

Answer 15

sorry sorry >.< simmer down!

Answer 16

no I am fine now........ok lets see if I can finish this problem

Answer 17

how about that second term? with the pi^2?

Answer 18

got it!!!! Finally
ok so I got

Answer 19

\[V ' = 60 \pi r - 6 \pi^2 r^2\]

Answer 20

\[60 \pi r - 6 \pi^2 r^2=0\]
\[6 \pi r = 0 \therefore r = 0\]
\[10-\pi r = 0 \therefore r =\frac{ 10 }{ \pi }\]

Answer 21

oo nice c:

Answer 22

since the want the max it is 10/pi

Answer 23

Thank You :)

Answer 24

I really appreciate your help

Answer 25

There was the other value, yes?
r=0.
But that minimizes I guess.

Answer 26

yes but it wants the max

Answer 27

cool c: