Question 1027528
{{{system(S=2*pi*rh+2*pi*r^2,h=2r)}}}
THE SECOND EQUATION IS IN THE PROBLEM DESCRIPTION!!



(a) Find the function S(r), surface area as a function or r.
SUBSTITUTE FOR h ACCORDING TO THE PROBLEM DESCRIPTION:
{{{S(r)=2*pi*r(2r)+2*pi*r^2}}} through substitution;
{{{S(r)=2*2*pi*r*r^2+2*pi*r^2}}}
{{{highlight(S(r)=4*pi*r^3+2*pi*r^2)}}}



(b) Find surface area as a function of cylinder height, h.
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{{{h=2r}}}
{{{h/2=2r/2}}}
{{{h/2=r}}}
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Substitute for h in S.
{{{S(h)=2*pi(h/2)*h+2*pi*(h/2)^2}}}
{{{S(h)=2*pi*h*h/2+2*pi*h^2/(2*2)}}}
{{{highlight(S(h)=pi*h^2+(pi*h^2)/2)}}}