Show that the right circular cone of least curved surface and given volume has an altitude equal to `sqrt(2)`time the radius of the base.

Explanation

To show that the right circular cone of least curved surface area and given volume has an altitude equal to \(\sqrt{2}\) times the radius of the base, we can follow these steps:

### Step 1: Set up the problem
Let the radius of the base of the cone be \(r\) and the height (altitude) of the cone be \(h\). The volume \(V\) of the cone is given by the formula:
\[ V = \frac{1}{3} \pi r^2 h \]
Since the volume is fixed, we can express \(h\) in terms of \(r\):
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