How is the "subtraction method" used to derive the formula for volume of a cylinder?

The subtraction method is used to find the volume of the cylinder by recalling that the volume of the cylinder consist of the volume of the cone and the volume of the sphere.

Step-by-step explanation:

In the subtraction method, we have that a cylinder of radius r, equal to that of a circle, and height 2·r consist of a cone of base radius r and height 2·r and a sphere of radius r as follows;

Volume or sphere of radius r = Volume of cylinder of radius r and height 2·r - Volume of cone of base radius r and height 2·r

∴ 4/3·π·r³ = Volume of cylinder of radius r and height 2·r  - 2/3·π·r³

Hence, volume of cylinder of radius r and height 2·r = 4/3·π·r³ + 2/3·π·r³ = 2·π·r³

Hence the subtraction method is used to find the volume of the cylinder by recalling that the volume of the cylinder consist of the volume of the cone and the volume of the sphere.