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Show that the height of the cone of maximum volume that can be inscribed in a sphere of radius 12 cm is 16cm.

Show that the height of the cone of maximum volume that can be inscribed in a sphere of radius 12 cm is 16cm.

Grade:12

2 Answers

Sher Mohammad IIT Delhi
askIITians Faculty 174 Points
6 years ago
Think of a unit circle in polar coordinates, with the pole on the circle.

r = cos u; So what you want is to maximize

r^3(sin u)^2(cos u) that is (cos u)^4(sin u)^2.

If x = sin u, you want to maximize x(1-x^2) = x - x^3. The max is for x = 1/sqrt(3). Then (cos u)^2 = 1 -x^2 = 2/3.

So 2/3 * 24 = 16.
Arun Kumar IIT Delhi
askIITians Faculty 256 Points
6 years ago
Hi


Thanks & Regards, Arun Kumar, Btech,IIT Delhi, Askiitians Faculty

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