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Wednesday, August 27, 2014

More Cylinder Problems, 7

Category: Solid Geometry

"Published in Newark, California, USA"

The crown of a straw hat has a base of 38 sq. in. The depth of the crown is 3 in. (Inside dimensions are given.) If the head occupies two-thirds of the space enclosed by the crown, find the volume remaining for ventilation. 

Photo by Math Principles in Everyday Life

Solution:

Consider the given figure above

Photo by Math Principles in Everyday Life

Since the area of the base or crown of a straw hat as well as the depth of the crown are already given, then we can get the volume of the crown of a straw hat as follows
 
 
 
 
If the head occupies two-thirds of the space or volume of the crown, then the volume remaining for the ventilation is one-third of the space of the crown.
 
Therefore,