Hello,

please help me,

Show that the right circular cone of least curved surface and given volume has an altitude equal to 2^(1/2) time the radius of the base?

Printable View

- Oct 21st 2009, 09:02 AManilpadavilright circular cone
Hello,

please help me,

Show that the right circular cone of least curved surface and given volume has an altitude equal to 2^(1/2) time the radius of the base? - Oct 21st 2009, 11:44 AMearboth
**[1]**Volume of the cone

**[2]**Area of the curved surface.

Solve [1] for r and plug in this term into [2]:

Now differentiate a wrt h (V is a constant!). You'll get:

Solve a'(h) = 0 for h. This is obviously only possible if

Solve for h. Substitute V by the term of [1] and solve for h again. You'll get

Remark: Especially the differentiation of a is really horrible. So I hope for you that someone knows a simpler, shorter way to solve the question. - Oct 21st 2009, 05:27 PManilpadavil
anyone knows a simpler way to solve the question