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Saturday, January 31, 2015

Right Circular Cylinder Problems, 12

Category: Solid Geometry

"Published in Newark, California, USA"

A wedge ABCDEF (see figure) is cut from a right circular cylindrical block of altitude 10 in. and radius 4 in. The dihedral angle of the wedge is 30°. Calculate its volume and total surface.

Photo by Math Principles in Everyday Life

Solution:

To analyze more the problem, it is better to label further the given figure as follows

Photo by Math Principles in Everyday Life

In this problem, we will use the given angle in solving for the length of an arc as well as the area of a circular sector. The given angle should be expressed in radians because it is a unitless value. 

The area of a circular sector DEF is






Therefore, the volume of wedge ABCDEF is




The length of arc EF is






Therefore, the total surface area of wedge ABCDEF is