a cylinder is inscribed inside a sphere with radius R. let x=height of cylinder. write a formila for the volume of the cylinder as a function of x and that includes R in some way. What is the domain of V(x) and graph V(x) when R=3
i have something like pi(4(R^2)-x^2)x/4....is this correct?
im having trouble with the domain and how to get that when we have two variables....
2007-09-18 04:14:01 · 2 answers · asked by Harmlessly Roaming 1 in Science & Mathematics ➔ Mathematics
R = radius of sphere
2007-09-18 05:18:11
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answer #1
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answered by ironduke8159 7
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x = height of cylinder
r = radius of cylinder
V = volume of cylinder
R^2 -(x/2)^2= r^2
V = pi r^2 x
V = pi(R^2 -(x/2)^2)x
|r|
Don't think of R as a variable. Consider it a constant, since the sphere is given with radius R.
Since x is the height of the cylinder, its necessary that x is zero or positive. And the cylinder has to be INSIDE the sphere, so at most x can be the diameter of the sphere, 2R.
Domain: 0 < x < 2R
Your formula looks great.
2007-09-18 12:03:45 · answer #2 · answered by mathgoddess83209 3 · 0⤊ 0⤋