# Thread: volume of sphere with hole in it

1. ## 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

2. 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.

3. 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

4. 4/3pi(13)^3-4/3pi(7)^3

8788pi/3-1372pi/3

2472pi

5. 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.

6. 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: $\displaystyle V=2\pi\int_0^{2\sqrt{30}}y^2-120\,dy$ (Do you see why?)