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.
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Question 1011918: 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. Found 2 solutions by josgarithmetic, ikleyn:Answer by josgarithmetic(39621) (Show Source):
x will be the radius of the CYLINDER.
The cylinder height will be .
That only gives you a figure for the largest cross section; but you want VOLUME, so....
, because the base radius for the cylinder is x.
Substitute for y.
-----No really - My mistake was to forget accounting for both parts of what make the "height". This would be 2y, instead of just y. The tutor iklyen gave the correct answer, result.
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.
-------------------------------------------------------------------- Comment from student: Thanks. Please show me how you derive the height algebraically.
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My responce
It is not algebraically.
It is geometrically.
Make a sketch of the section of the sphere with the cylinder inscribed.
Then apply the Pythagorean Theorem.
It is so obvious.
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