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Friday, January 11, 2013

Right Circular Cylinder - Right Circular Cone

Category: Solid Geometry

"Published in Newark, California, USA"

The solid shown consists of a right circular cylinder of diameter d and altitude h, surmounted by a cone of diameter  of base d and altitude h/2. 

(a) Write a formula for the volume.

(b) Find the volume, given d = 4.42 in. and h = 5.17 in.


Photo by Math Principles in Everyday Life

Solution:

Consider the volume of right circular cylinder



Consider the volume of right circular cone



If h = h/2, then





The combination of the volume of right circular cylinder and right circular cone is








If r = d/2, then the equation becomes










If d = 4.42 in. and h = 5.17., then the volume is