__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.

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__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