SOLUTION: A sphere of diameter 40cm has a cylinder of base radius r cm inscribed within it. Find an expression for teh volume of the cylinder, V(r), in terms of r only.

Algebra ->  Volume -> SOLUTION: A sphere of diameter 40cm has a cylinder of base radius r cm inscribed within it. Find an expression for teh volume of the cylinder, V(r), in terms of r only.      Log On


   

Question 1013226: A sphere of diameter 40cm has a cylinder of base radius r cm inscribed within it. Find an expression for teh volume of the cylinder, V(r), in terms of r only.
Answer by josgarithmetic(39631) About Me  (Show Source):
You can put this solution on YOUR website!
Cross section through the middle can be a circle and if centered at the Origin for graphing, x%5E2%2By%5E2=20%5E2.

x=r and use r, as if a constant, to find y.

Volume of the cylinder will be 2%2Ay%2Api%2Ar%5E2; you'll need the picture to see this.

r%5E2%2By%5E2=400
y=sqrt%28400-r%5E2%29

volume is 2pi%2Asqrt%28400-r%5E2%29r%5E2-----answer
Do not confuse radius of the circle or sphere with the radius of the cylinder.