SOLUTION: this question is not out of the book... Find what the minimum surface area for a cylindrical can will be to hold {{{500 cm^3}}}. Give the radius and the height. {{{surface ar

Algebra ->  Rational-functions -> SOLUTION: this question is not out of the book... Find what the minimum surface area for a cylindrical can will be to hold {{{500 cm^3}}}. Give the radius and the height. {{{surface ar      Log On


   

Question 37163: this question is not out of the book...
Find what the minimum surface area for a cylindrical can will be to hold 500+cm%5E3. Give the radius and the height.
surface+area-+2%28pi%29r%5E2%2B2%28pi%29rh
volume-%28pi%29r%5E2h
Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
Since we wish to minimize surface area, we will need to find r when dA/dr = 0.
(1) A = 2(pi)r^2 + 2(pi)rh
We can find h in terms of r by considering the volume formula
V = (pi)r^2h
500 = (pi)r^2h
h = 500/(pi)r^2
Substituting into (1) above, we get
A = 2(pi)r^2 + 2(pi)r(500/(pi)r^2)
A = 2(pi)r^2 + 1000/r
Now take dA/dr and set it equal to zero.
dA/dr = 4(pi)r - 1000/r^2 = 0
And r = cube root of (250/pi)
From there you can find h and A.