# The Sphere

Sphere is a solid bounded by closed surface every point of which is equidistant from a fixed point called the center.

**Properties of a Sphere**

- Every section in the sphere made by a cutting plane is a circle. If the cutting plane passes through the center of the sphere, the section made is a
*great circle*; otherwise the section is a*small circle*. - For a particular circle of a sphere, the
*axis*is the diameter of the sphere perpendicular to the plane of the circle. - The ends of the axis of the circle of a sphere are called
*poles*. - The nearer the circle to the center of the sphere, the greater is its area.
- The largest circle in the sphere is the great circle.
- The radius (diameter) of the great circle is the radius (diameter) of the sphere.
- All great circles of a sphere are equal.
- Every great circle divides the sphere into two equal parts called
*hemispheres*. - The intersection of two spherical surfaces is a circle whose plane is perpendicular to the line joining the centers of the spheres and whose center is on that line. (See figure to the right.)
- A plane perpendicular to a radius at its extremity is tangent to the sphere.

**Formulas for a Sphere**

**Surface Area, A**

The surface area of a sphere is equal to the area of four great circles.

$A = 4\pi R^2$

$A = \pi D^2$

**Volume, V**

$V = \frac{4}{3}\pi R^3$

$V = \frac{1}{6}\pi D^3$