A cylindrical can, open at the top, is to hold 470cm^{3} of liquid. Find the height and radius that minimize the amount of material needed to manufacture the can. Enter your answer with rational exponents, and use pi to represent pi. Radius = ? Height = ?

Globokim8 2021-02-26 Answered
A cylindrical can, open at the top, is to hold 470cm3 of liquid. Find the height and radius that minimize the amount of material needed to manufacture the can. Enter your answer with rational exponents, and use pi to represent pi.
Radius =?
Height =?
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Expert Answer

coffentw
Answered 2021-02-27 Author has 103 answers
Given:
V=470cm3
We have to find height and radius
V=πr2h=470
h470πr2
Plug this into the surface area equation
SA=πr2+2πrh
=πr2+2πr(470πr2)
=πr2+940r
Differentiate SA and set to 0 solve for r
dSAdr=2πr940r2=0
2πr=940r2
r3=9402x
r3=470π
r=(470π)13
=5.30cm
Now, we find h:
h=470πr2
=470π(5.30)2
=5.32cm
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