Cylindrical hole of radius a is bored through a sphere of radius 2a. the surface of the hole passes through the center of the sphere. how much material is removed

The amount of material removed is the volume of the region within the sphere bounded by the cylinder. Consider a sphere of radius centered at the origin; this sphere has equation

The given cylinder has equation

The volume of the region of interest is given by

Converting to cylindrical coordinates, setting

we have

and

where is the Jacobian of the transformation from to . The region is described by the set

The integral is then

The integral with respect to is symmetric about , so we instead compute twice the integral from to , and we can immediately compute the integral with respect to :

Now, let , so that :

6.9

step-by-step explanation:

simple math really

6 1/2 times 0.6 = 3.9

but if you are just doing 6 and not 6 1/2 then the answer is 3.6

my answer got deleted but it's a

step-by-step explanation: