Verified answer

A = 2 π (r² + r h)

V = πr²h or h = V/πr²

A = 2 π [ r² + 100/(πr) ]

dA/dr = 2 π [ 2r - 100/(πr²) ]

d²A/dr² = 2 π [ 2 + 200/(πr³) ] .... will be positive, so dA/dr = 0 is a min.

0 = [ 2r - 100/(πr²) ] ............... find a min by setting dA/dr = 0

100 = 2πr³

r = (50/π)^(1/3)

Answer: r = (50/π)^(1/3) ≈ 2.515, h = 20 / [ (20π)^(1/3) ] ≈ 5.03

How can I type the formulas here? Do you know?

Anyway, to answer your question. You have the volume condition as Pi(r^2)*height = 100. So height = 100 / [Pi(r^2)] (formula #1). Now you need to minimize 2(Pi*(r^2)) + 2Pi*r*height (formula #2). Substitute Formula #1 into formula #2. And solve for derivative.

There you will find your answer. Sorry for this description. I haven't figured out how to type formula in Firefox.

2(pi r 2) + (2 pi r)* h 2(16pi) + 5(8pi) one hundred.40 8 + one hundred twenty five,6 226.08 cm2 226.08 x 5 $a million,one hundred thirty.4 those are tough. use definitely pi not 3.14. like i did. yet this is common thank you to get the respond ... sturdy success