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Spheres
Introduction: We examine the 3-dimensional object known as a sphere.

Definitions:
A sphere is a 3-dimensional solid which comprises all points in space that are equi-distant from one point called the center of the sphere. The distance (sometimes the line segment itself) is called the radius of the sphere. We show sphere P below. It is named P because P is the center of the sphere. The radius r is the segment (distance) PQ.

The Lesson:
Two important formulas help us measure the size of a sphere. In the sphere shown above, suppose that r = PQ = 5 inches in length. The volume would be given by
.
While the surface area would be given by
.
Let's Practice:
1. If a sphere has radius 9 meters, what are the surface area and the volume?
To find surface area, we use
.
To find the volume, we use
.
1. Suppose a sphere has a surface area of . What is the volume?
We have surface area = . We solve for r by dividing both sides of this equation by . This gives us
.
To calculate the volume we use
.

Examples
 A sphere has a radius of 7 feet. What are its surface area and volume? What is your answer?
 A sphere has a volume of . What is the surface area? What is your answer?

M Ransom

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