Amachine part consists of a half sphere and a cylinder, as shown in the figure. the total volume of the part is
cubic inches.

A machine consist of a half sphere and a cylinder, so the total volume is going to be given by:

Volume = Cylinder [in^3] + Half-sphere [in^3]

The volume of a cylinder is given by:

Vcylinder = πr^2h, where:

h: Height of the cylinder [in]

r: radius of the cylinder [in]

The volume of a sphere is given by:

Vsphere= 4/3πr^3, where:

r: Radius of the sphere [in]

Given that the machine consistsof a half sphere, then the radius of the half sphere is:

Vhalf-sphere= 4/6πr^3.

Therefore, the total volume is:

Total volume = Vhalf-sphere + Vcylinder

Total volume = 4/6πr^3 + πr^2h [inches^3]