A hole of radius 1 is drilled to the centre of a ball of radius 2

Question

A hole of radius $1$ is drilled into the centre of a sphere of radius $2$.

Calculate the remaining volume.

Could someone explain to me how to approach this. I don't need a specific answer.

I know it involves integration but my method creates a doughnut shape revolving around the x-axis and that's clearly not right.

Thanks !

EDIT:

I've tried to create a semicircle from $x = -2 \rightarrow x = 2 $ which revolves around the x-axis. This gets me the total volume of the sphere. I then must subtract the integral of $y = \pi$? I'm unsure of this.

Answer 1

Hint: You can do this by revolution. Ball is revolved by $y= \sqrt{4-x^2}$, and the hole is revolved by $y=1$.

I think a figure will help

Is this what your concern is?