Question 959400
watch for the ratio between the height and the radius.  The diameter of the hole is 4 inches so the radius of the hole is 2 inches.  The conical portion removed in the hole drilling is a height of {{{2*(24/6)=8}}} inches heightl  The volume is {{{cross(8*pi*2^2=32pi)}}}{{{(1/3)pi*2^2*8=(32/3)pi}}}.  A purely cylindrical portion below this conical space is of volume  {{{(24-8)*pi*2^2=16*4*pi=64pi}}}.  The total space removed in the drilling is {{{(32/3)pi+64pi=(224/3)pi}}}.


New volume is original volume minus drilled-out volume.
{{{highlight(NewVolume=cross(24*pi*6^2-96pi))}}}{{{(1/3)pi*6^2*24-(224/3)pi}}}.
That is so you can understand.  Simplify from that.


(should be better now)