12.6 Surface Area and Volume of Spheres

Goal 1: Finding the Surface Area of a Sphere

Goal 2: Find the volume of a sphere

Sphere

A sphere is the locus of points in space that are a given distance from a point.

The point is called the center.

A radius of a sphere is a segment from the center to a point on the sphere.

Sphere

A chord of a sphere is a segment whose endpoints are on the sphere.

The diameter is a chord that contains the center.

Theorem 12.11 Surface Area of a Sphere

The surface area S of a sphere with radius r is

See example

24 rS

Ex. 1 Find the surface area of the sphere.

The mean of the radii for the earth is 3,959 miles.

Great Circle

A great circle is the largest circle cross section possible. It includes the center of the circle.

See example

Theorem 12.12 Volume of a Sphere

The volume V of a sphere with radius r is

See example

3

4 3rV

Ex. 1 Find the volume of the the planet Jupiter.

Diameter of Jupiter is 88,846 miles