<p>How do you do this problem?</p>
<p>Make a cone with a volume of 10 meters^3 with the LEAST Surface Area</p>
<p>V = (pi/3)(r^2)h = 10 m^3</p>
<p>A = pi<em>r</em>(r + sqrt(r^2 + h^2))</p>
<p>There are at least two ways to solve this problem using calculus. We may use Lagrange multipliers to find critical points, that is, critical points occur when</p>
<p>∇A = λ∇V, where λ is a non-zero constant. Then you’d have to find the partial derivatives ∂A/∂h, ∂A/∂r, etc.</p>
<p>The single-variable calculus solution involves writing h in terms of r (h = 30/(pi*r^2)), plugging it into the formula for A, then differentiating with respect to r. The solution takes fewer steps, but the function itself looks quite messy.</p>