# volume of sphere with hole in it

• Aug 7th 2009, 12:05 PM
dat1611
volume of sphere with hole in it
A ball of radius 13 has a round hole of radius 7 drilled through its center. Find the volume of the resulting solid.
so volume of a sphere 4/3pi(r^3)
but if u take the volume of both and subtract its not right
• Aug 7th 2009, 12:13 PM
skeeter
Quote:

Originally Posted by dat1611
A ball of radius 13 has a round hole of radius 7 drilled through its center. Find the volume of the resulting solid.
so volume of a sphere 4/3pi(r^3)
but if u take the volume of both and subtract its not right

show what you did.
• Aug 7th 2009, 12:15 PM
CaptainBlack
Quote:

Originally Posted by dat1611
A ball of radius 13 has a round hole of radius 7 drilled through its center. Find the volume of the resulting solid.
so volume of a sphere 4/3pi(r^3)
but if u take the volume of both and subtract its not right

see here

CB
• Aug 7th 2009, 12:17 PM
dat1611
4/3pi(13)^3-4/3pi(7)^3

8788pi/3-1372pi/3

2472pi
• Aug 7th 2009, 12:23 PM
skeeter
Quote:

Originally Posted by dat1611
4/3pi(13)^3-4/3pi(7)^3

8788pi/3-1372pi/3

2472pi

the part that's drilled out is not a sphere.
• Aug 7th 2009, 12:30 PM
skeeter
• Aug 9th 2009, 02:42 PM
Chris L T521
Quote:

Originally Posted by dat1611
A ball of radius 13 has a round hole of radius 7 drilled through its center. Find the volume of the resulting solid

can anyone give me an answer for this

The volume of the solid is given by: $V=2\pi\int_0^{2\sqrt{30}}y^2-120\,dy$ (Do you see why?)