## Monday, March 18, 2013

### More Right Circular Cylinder Problem, 2

Category: Solid Geometry

"Published in Newark, California, USA"

A right cylindrical solid of altitude 6 in. has the cross section shown in the shaded portion of the figure. BEDG is a circle whose radius is OG. AFCG is a circle which is tangent to the larger circle at G. If AB = CD = 5 in. and EF = 9 in., find the volume of the cylinder.

 Photo by Math Principles in Everyday Life

Solution:

The cross section of a right circular cylinder consists of two tangent circles with their common point at Point G. Let's further analyze and label the cross section of a right circular cylinder as follows

 Photo by Math Principles in Everyday Life

We noticed that line segments AC and FG are the chords of a small circle that intersect at point O, which is also the center of a big circle. From Plane Geometry, we know that the product of two divided chords is equal to the product of other two divided chords. We can solve for the radius of a big circle as follows

The line segment OF is calculated as follows

The radius of a small circle is calculated as follows

The area of the shaded portion of the cross section of a right circular cylinder is calculated as follows

Area of a base = Area of Big Circle - Area of Small Circle

Therefore, the volume of a right circular cylinder is

or