precalc…check/help?

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….

Top 1 Answers

A few days ago

Anonymous

Favorite Answer

let r = radius of the cylinder

r^2 = R^2 – (x/2)^2 by pythagoras

V = πr^2x

= π(R^2 – (x/2)^2)x

= π(4R^2 – x^2)x/4

so you’re correct

domain

R is a constant for the sphere not a variable

you need

x ≥ 0 so that V > 0 since negatve volumes don’t make sense

and

x ≤ 2R ie the diameter, other wise it wouldn’t be contained in the sphere

domain = { 0 ≤ x ≤ 2R }

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precalc…check/help?

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