Zus Principle is also known as Cavalieris principle Back in

Zu\'s Principle is also known as Cavalieri\'s principle

Back in 5th century China, the formulas for the volume of a cylinder and cone were known, but the formula for the volume of a sphere was just being tackled. Use Zu\'s Principle (see top of page 142 of text) to find the volume of the semisphere given that you know the formulas for the volume of a cylinder and the volume of a cone only. Use your results from above. d) e) Where have we seen this concept before?

Solution

Zu\'s Principle

volume of semisphere= volume of cylinder ( height and radius of cylinder equal to radius of sphere)

-(volume of cone) (base radius = radius of sphere)

volume of semisphere = pi*r²*(r) - (1/3)pi*r²*(r) =(2/3)*pi*r³

therefore volume of semisphere = (2/3)*pi*r³