Explain when each of the following formula adjustments might prove useful. a. dividing the volume formula for a sphere by two. b. dividing the volume formula for a rectangle prism by three.

We know that

Part a)
volume of a sphere=(4/3)*pi*r³
where r is the radius
When the volume formula of the sphere is divided by two, it is useful to find the volume of the hemisphere
so
volume of hemisphere=[(4/3)*pi*r³]/2> (2/3)*pi*r³

part b) volume of the rectangular prism=pi*B*h
where 
B is the area of the rectangular base
h is the height of the prism

When dividing the volume formula of a rectangular prism by three, it is useful to obtain the volume of a rectangular pyramid with the same base and the same height as the prism

volume rectangular pyramid=(1/3)*[pi*B*h]