SOLUTION: A cylinder is inscribed in a sphere of radius 1. a. Express the volume V of the cylinder as a function of the base radius r.

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Question 1011899: A cylinder is inscribed in a sphere of radius 1.
a. Express the volume V of the cylinder as a function of the base radius r.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
R= radius of the cylinder,
h= height of the cylinder.
A cross-section of the sphere, with the cylinder
(sliced along the middle) looks like this:
Applying the Pythagorean theorem, %28h%2F2%29%5E2%2BR%5E2=1%5E2-->%28h%2F2%29%5E2=1-R%5E2-->h%2F2=sqrt%281-R%5E2%29-->h=2sqrt%281-R%5E2%29 .
Since for a cylinder, Volume=pi%2AR%5E2%2Ah ,
highlight%28Volume=2pi%2AR%5E2%2Asqrt%281-R%5E2%29%29