Question

Please help me out. :)

Find the dimensions of the right circular cone of least volume that can circumscribed about a sphere of radius a.
(HINT: let x + 2a be the altitude)

Answer 1

Let R be the base radius of the cone, h its height and α the half angle at the apex (i.e the angle between the symmetry axis of the cone and its side). Then:

h = r(1+sinα)/sinα

R = r(1+sinα)/cosα

Volume of cone = V = ⅓πr³(1+sinα)³/(cos²α.sinα)

You need to take dV/dα, set it = 0 (for a minimum) and solve for α which will give you the values of h and R from the above formulae.

Answer 2

hope that helps

Answer 3

is there any easy solution?