Question 383609
{{{S = pi*r^2 + pi*r*sqrt(r^2 + h^2)}}}
Differentiate with both {{{r}}} and {{{h}}} as variables. 
{{{dS=2*pi*r*dr+pi*r*(1/(2*sqrt(r^2+h^2)))*(2r*dr+2h*dh)+ pi*sqrt(r^2+h^2)*dr}}}

Substitute {{{r=3}}}, {{{h=4}}}, {{{dr=dh=0.25}}},
{{{dS=2*pi*3*(0.25)+pi*3*(1/(2*sqrt(3^2+4^2)))*(2(3)*(0.25)+2(4)*(0.25))+ pi*sqrt(3^2+4^2)*(0.25)}}}
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{{{dS=(3/2)*pi+pi*3*(1/(2*5))*(3/2+2)+ pi*(5/4)}}}
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{{{dS=pi*((3/2)+(21/20)+(5/4))}}}
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{{{dS=pi*((30/20)+(21/20)+(25/20))}}}
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{{{dS=(19/5)*pi}}}{{{cm^2/s}}}