Calculus II: A bead is formed from a sphere of radius 4 by drilling through a diameter of the sphere with a drill bit of radius 1. Find the volume of the bead.

Question

anonymous · Answer

I am not sure if we need any calculus for this

anonymous · Answer

oh okay, I was just indicating that this was from my calculus 2 class.

andrew314 · Answer

You coud probably do it without calculus, but the volume of the cylinder has a parabola rotated about the y-axis on the top and bottom. Like a lens shape? I don't remember what to call it, as it's been a while since I've taken calc 2.

andrew314 · Answer

I don't have much time to write a proper answer, but I would calculate the volume of the cylinder, using normal geometry formula. Then calculate the volume of the cylinder, using the shell method, probably (like I said, it's been a long time since I took calc 2 so I'm not sure if it that's the best way) and subtract that from your sphere volume.

anonymous · Answer

ok

anonymous · Answer

http://www.sfu.ca/~adebened/funstuff/sphere_cyl.pdf

anonymous · Answer

thanks robtobey

anonymous · Answer

okay thank you Pross

anonymous · Answer

http://mathworld.wolfram.com/SphericalCap.html A formula for a "Spherical Cap" is presented at the above web site, line (2). The volume removed from the sphere is the sum of the cylinder's volume and twice one of cap's volume.

anonymous · Answer

|dw:1324153859063:dw|