Question 160801
{{{SA=4*pi*R^2}}}
You're looking for the rate of change of SA with respect to R. 
That's the same as the derivative.
Take a small step in R, calculate the SA, subtract the original SA, and divide by the small step. 
{{{SA(R+dR)=4*pi*(R+dR)^2=4*pi*(R^2+2RdR+dR^2)}}}
{{{SA(R)=4*pi*R^2}}}
{{{(SA(R+dR)-S(R))/dR=(4*pi*(R^2+2RdR+dR^2-R^2))/dR}}}
Assume that {{{dR}}} is small, then {{{dR^2}}} is even smaller (=0)
{{{(SA(R+dR)-S(R))/dR=(4*pi*(2RdR+cross(dR^2)))/dR}}}
{{{(SA(R+dR)-S(R))/dR=8*pi*R}}}
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That's the hard way to find the derivative of SA with respect to R. 
You can also differentiate.
{{{SA=4*pi*R^2}}}
{{{d(SA)/dR=8*pi*R}}}
So when R=20
{{{d(SA)/dR=8*pi*20=160*pi}}}