Question 842348
This analysis assumes just the wall cylinder without any top or bottom.


r=2h, r is radius and h is height or tallness.
Volume is {{{h*pi*r^2=164}}}
{{{(r/2)pi*r^2=164}}}
{{{(1/2)pi*r^3=164}}}
{{{pi*r^3=328}}}
{{{r=root(3,328/pi)}}}
{{{highlight(r=2*root(3,41/pi))}}}
This means {{{highlight(h=root(3,41/pi))}}}


The surface area of just the tube part without any top or bottom:
{{{(2*pi*r)*h}}} which is circumference by "length".
Substitute the values found.
-
Those Substitutions:
{{{2*pi*(2*root(3,41/pi))(root(3,41/pi))}}}
{{{highlight(4*pi(root(3,41/pi))(root(3,41/pi)))}}}
-
A separate substep, {{{root(3,41/pi)=root(3,13.050705)=highlight_green(2.3544)}}}
-
Surface area may be represented {{{4*pi*2.3544*2.3544}}}
{{{4*pi*5.54314}}}...
{{{highlight(22.1725*pi)}}}