Question 1137934
<br>
{{{V = (pi)(r^2)(h) = 10}}} (1)<br>
{{{S = 2(pi)(r^2)+2(pi)(r)(h)}}} (2)<br>
Solve equation (1) for h in terms of r and substitute into equation (2), giving you an expression in terms of r only for the surface area.<br>
{{{h = 10/((pi)(r^2))}}}
{{{S = 2(pi)(r^2)+2(pi)(r)(10/((pi)(r^2))) = 2(pi)(r^2)+20/r}}}
{{{dS/dr = 4(pi)(r)-20/r^2}}}<br>
Set the derivative equal to 0 and solve.<br>
{{{4(pi)(r)-20/r^2 = 0}}}
{{{4(pi)(r) = 20/r^2}}}
{{{r^3 = 20/(4(pi)) = 5/(pi)}}}
{{{r = (5/(pi))^(1/3)}}}