Question 1105150
You probably mean,  surface area is {{{16pi}}} square centimeters.


{{{h=r+4}}}
&
Total Area, {{{2pi*rh+pi*r^2}}}


The question asks for solving for {{{2r}}}.


{{{2pi*rh+pi*r^2=16pi}}}
{{{2pi*r(r+4)+pi*r^2=16pi}}}
Divide both members by {{{2pi}}};
{{{r(r+4)+(1/2)r^2=8}}}

{{{r^2+4r+(1/2)r^2=8}}}

{{{(3/2)r^2+4r-8=0}}}

{{{highlight_green(3r^2+8r-16=0)}}}


{{{r=(-8+sqrt(64+4*3*16))/6}}}

{{{r=(-8+sqrt(256))/6}}}

{{{r=(16-8)/6}}},   {{{r=4/3}}}

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Diameter, {{{2r=8/3}}}

{{{highlight(2r=2&2/3)}}}, in centimeters.