Posted by **Jeff** on Tuesday, February 12, 2008 at 12:19am.

A ball of radius 10 has a round hole of radius 5 drilled through its center. Find the volume of the resulting solid.

- calculus -
**Meli**, Tuesday, February 12, 2008 at 12:22am
First you find the volume of the whole ball, then the volume of the round hole inside, then, you subtract the hole's volume from the whole ball's volume, leaving you with the volume of the resulting solid.

- calculus -
**drwls**, Tuesday, February 12, 2008 at 12:32am
Perform a volume integration with the center of the sphere at the origin and the circular hole aligned with the z-axis. The integration will end at +/-a, where

a^2 = 10^2 - 5^2 = 75

a = 5 sqrt 3 = 8.6603

The volume will be twice the volume above the x-y plane.

V = 2*INTEGRAL pi (r^2 - 5^2) dz

(z = 0 to 8.6603)

r^2(z) = 100 - z^2

## Answer this Question

## Related Questions

- 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 12 has a round hole of radius 6 drilled through its ...
- physics - A curcial part of a piece of machinery starts as a flat uniform ...
- calculus - Find the volume that remains after a hole of radius 1 is bored ...
- calculus 1 (I need help) - The portion of the ellipse x^2/9+y^2/4=1 with x ...
- Physic - A machine part is made from a uniform solid disk of radius R = 0.161 m ...
- Physics - A machine part is made from a uniform solid disk of radius R and mass ...

More Related Questions