Wednesday

October 22, 2014

October 22, 2014

Posted by **Jane** on Thursday, December 8, 2011 at 1:34pm.

- calculus -
**Steve**, Thursday, December 8, 2011 at 4:50pmA little investigation will lead you to the formula that if a hole of radius r is drilled through a sphere of radius R, the remaining volume is just 4pi/3 (R^2 - r^2)^(3/2)

In this case, that would be 4pi/3 * 3√3 = 4√3 pi

__________________________

You might also look up the napkin ring problem, where it is shown that if a hole of length h is drilled through a sphere, the remaining volume is independent of the radius of the sphere!

In this case, h/2 = R^2 - r^2 = √3, so h = 2√3

The remaining volume is pi/6 h^3 = pi/6 * 24√3 = 4√3 pi

- calculus -
**Jane**, Friday, December 9, 2011 at 3:07pmthanks!

**Answer this Question**

**Related Questions**

Calculus - A ball of radius 12 has a round hole of radius 6 drilled through its ...

Calculus - A ball of radius 14 has a round hole of radius 8 drilled through its ...

calculus 2 - A ball of radius 12 has a round hole of radius 6 drilled through ...

calculus - A ball of radius 10 has a round hole of radius 8 drilled through its ...

Calculus - A ball of radius 16 has a round hole of radius 4 drilled through its ...

calculus - A ball of radius 10 has a round hole of radius 5 drilled through its ...

calculus - 3. The radius r of a sphere is increasing at a constant rate of 0.04 ...

physics - A curcial part of a piece of machinery starts as a flat uniform ...

calculus *improper integrals* - A hole of a radius of 1cm is pierced in a sphere...

Calculus - 4. At time t, t>0, the volume of a sphere is increasing at a rate ...