T = angle up from center of sphere to intersection of cylinder and sphere
r = 10
height of cylinder = 2 r sin T
radius of cylinder = r cos T
volume of cylinder =
V = pi(r^2 cos^2 T)(2 r sin T)
= 2pi r^2 (cos^2 T sin T)
dV/dT = 0 for max
= cos^3 T - 2 sin^2T cos T
= cosT ( cos^2 T - 2 sin^2 T
so for max
2 sin^2 T = cos^2 T
sin^2 T/cos^2 T = tan^2 T = 1/2
or
tan T = sqrt 2/2
T = 35.3 degrees3
height = 2 r sin T = 11.6
radius = r cos T = 8.16
Find the dimension of the right circular cylinder of the largest volume that can inscribed in a
Sphere of radius 10 units.
1 answer
1 answer