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SPHERES

A SPHERE is a solid figure with all points on its surface equally distant from its center.

Figure 18-19.-Parts of a sphere.

In figure 18-19, the center of the sphere is point 0. 

A RADIUS of a sphere is a straight line segment joining the center of the sphere to a point on the surface. Lines OA, OB, OC, OD, OE, and OF in figure 18-19 are radii. A DIAMETER of a sphere is a straight line segment joining two points on the surface and passing through the center of the sphere. Lines AB, CD, and EF in figure 18-19 are diameters. A HEMISPHERE is half of a sphere.

Circles of various sizes may be drawn on the surface of a sphere. The largest circle that may be so drawn is one with a radius equal to the radius of the sphere. Such a circle is a GREAT CIRCLE. In figure 18-19, circles AEBF, ACBD, and CEDF are great circles. 

On the surface of a sphere, the shortest distance between two points is an arc of a great circle drawn so that it passes through the two points. This explains the importance of great circles in the science of navigation, since the earth is approximately a sphere.

Surface Area

The surface area of a sphere may be calculated by multiplying 4 times ‘II times the square of the radius. Written as a formula, this is

A = 4pr2

The formula for the surface area of a sphere may be rewritten as follows:

A = (2nr)(2r)

When the formula is factored in this way, it is easy to see that the surface area of a sphere is simply its circumference times its diameter.

Volume

The volume of a sphere whose radius is r is given by the formula

EXAMPLE: Find the volume of a sphere whose diameter is 42 inches.

SOLUTION:

Practice problems. Calculate the surface

area and the volume of the sphere in each of

the following problems:

1. Radius = 7 inches 
2. Radius = 14 cm

Answers:

1. Area = 615 sq in. (approx.)
Volume = 1436 cu in. (approx.)

2. Area = 2462 sq cm (approx.)
Volume = 11,489 cu cm (approx.)




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