## Friday, March 8, 2013

### Sphere - Circular Section Problem

Category: Solid Geometry

"Published in Newark, California, USA"

Find the area of a section cut from a sphere of radius R by a plane distant R/2 from the center of the sphere.

 Photo by Math Principles in Everyday Life

Solution:

From the given figure above, we need to get the radius of the circular section in order to get its area. Let's consider the following procedures in order to get the radius of a circular section.

From point O which is the center of a sphere, draw a vertical line and label its end as point A.

At the end of a circular section, label as point B and then connect to the center of a sphere at point O. OB is also the radius of a sphere. In this case, OB = R.

From point B, draw a horizontal line towards to line OA and label their intersection as point C. CB is the radius of a circular section. In this case, CB = r.

Finally, label further the above figure as follows

 Photo by Math Principles in Everyday Life

To solve for r which is the radius of the circular section, use Pythagorean Theorem as follows

Therefore, the area of a circular section is