# calculus

posted by .

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

• calculus -

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 -

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

## Similar Questions

1. ### physics

A curcial part of a piece of machinery starts as a flat uniform cylindrical disk of radius R0 and mass M. It then has a circular hole of radius R1 drilled into it. The hole's center is a distance h from the center of the disk. Find …
2. ### Calculus

A ball of radius 16 has a round hole of radius 4 drilled through its center. Find the volume of the resulting solid.
3. ### calculus

A ball of radius 10 has a round hole of radius 8 drilled through its center. Find the volume of the resulting solid.
4. ### Calculus

A ball of radius 12 has a round hole of radius 6 drilled through its center. Find the volume of the resulting solid. I tried finding the volume of the sphere and the volume of the cyclinder then subtract however that did not work.
5. ### calculus 2

A ball of radius 12 has a round hole of radius 6 drilled through its center. Find the volume of the resulting solid.
6. ### Calculus

A ball of radius 14 has a round hole of radius 8 drilled through its center. Find the volume of the resulting solid
7. ### Physics

A machine part is made from a uniform solid disk of radius R and mass M. A hole of radius R/2 is drilled into the disk, with the center of the hole at a distance R/2 from the center of the disk (the diameter of the hole spans from …
8. ### Physic

A machine part is made from a uniform solid disk of radius R = 0.161 m and mass M = 7.75 kg. A hole of radius R/2 is drilled into the disk, with the center of the hole at a distance R/2 from the center of the disk (the diameter of …
9. ### calculus

Find the volume that remains after a hole of radius 1 is bored through the center of a solid sphere of radius 2.
10. ### calculus 1 (I need help)

The portion of the ellipse x^2/9+y^2/4=1 with x greater than or equals to 0 is rotated about the y-axis to form a solid S. A hole of radius 1 is drilled through the center of S, along the y-axis. Find the exact volume of the part of …

More Similar Questions