The volume of the cone is 6 cubic inches. What is the height of a cone with the same base diameter but a volume of only 3 cubic inches?

We have  that

6 =  (1/3)pi r^2 h

Note that if we (1/2) the  height, the new volume  is

[(1/3) pi *r^2 (1/2)h ]  =  [ (1/3) pi r^2 h ] (1/2)  =    [ 6 ] (1/2)  = 3

So  the height of the cone with a volume of 3 is (1/2) the height of the cone with a volume of 6