SOLUTION: A cylinder is inscribed in a sphere of radius 1. Express the volume V of the cylinder as a function of the base radius r. (The final answer must not contain any variable other than
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Question 1011932: A cylinder is inscribed in a sphere of radius 1. Express the volume V of the cylinder as a function of the base radius r. (The final answer must not contain any variable other than r. Please show all steps including algebra clearly) Found 2 solutions by dkppathak, ikleyn:Answer by dkppathak(439) (Show Source):
You can put this solution on YOUR website! A cylinder is inscribed in a sphere of radius 1. Express the volume V of the cylinder as a function of the base radius r. (The final answer must not contain any variable other than r. Please show all steps including algebra clearly)
let base radius of cylinder is r
radius of sphere is 1 given
height of cylinder will be 2 unit
volume of cylinder = pie r^2h= pie r^2x2 =2pie r^2
can be solved further use pie=3.14 or 22/7
2x22xr^2/7=44r^2/7
or
2x3.14r^2=6.28r^2
You can put this solution on YOUR website! .
A cylinder is inscribed in a sphere of radius 1. Express the volume V of the cylinder as a function of the base radius r.
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Volume of a cylinder is
V = , (1)
where r is the radius of the cylinder and h is the height of the cylinder.
When cylinder of the radius r is inscribed in a sphere of radius r,
h = (2)
(make a sketch and apply the Pythagorean theorem).
Substitute (2) into (1), and you will get
V = .
This is the required formula.
