<span>Generate a function for the height of the cyliner as a function of radius. Use this function to generate a function of r for the material used. Take the derivative of that function, set it to zero, and solve for r.
</span><span>V=πr2h</span>h=d h=d=2r h=2r <span>V=πr22r
</span><span>V(r,h)=180.5=πr2h⟹h=<span>180.5/<span>πr2</span></span></span><span>⟹A(r)=r(r+h)=r2+<span>180.5/<span>πr
</span></span></span><span>A(r)=2r(2r+h)=4r2+<span>361/<span>πr
</span></span></span>
<span>A′(r)=8r−<span>361/<span>π<span>r2</span></span></span></span>