Sec. 12.6: Surface Area and Volume of Spheres A sphere is the set of all points in space equidistant from a given point, called the center of the sphere. A radius of a sphere is a segment from the center to a point on the sphere.

A chord of a sphere is a segment whose endpoints are on the sphere. A diameter of a sphere is a chord that contains the center.

Examples 1 The diameter of a sphere is 40 feet. Find the surface area of the sphere. 1600π ft 2 ≈ ft 2

Examples 2 The surface area of a sphere is 30π square meters. Find the radius of the sphere. r ≈ 2.74 m

Example 3 If the circumference of a sphere is 6π feet, find the surface area of the sphere. 36π ft 2 ≈ ft 2

Example 4 The radius of a sphere is 5 yards. Find the volume of the sphere. (500/3)π yd 3 ≈ yd 3

Example 5 Find the radius of a sphere with a volume of 288π in 3. What about if volume is 288 in 3 ? r ≈ 6 in If volume is 288 in 3, then r ≈ in

Example 6 A solid consists of a hemisphere of radius 1 meter on top of a cone with the same radius and height 5 meters. Find the volume of the solid. (7/3)π m 3 ≈ 7.33 m 3