Chapter 11: Surface Area & Volume 11.6 Surface Area & Volume of Spheres

Definitions Sphere: –set of all points in space equidistant from a given point called the center Radius: –segment that has one endpoint at the center and the other endpoint on the sphere Diameter: –a segment passing through the center with endpoints on the sphere

Definitions when a plane intersects a sphere, the cross section is a circle great circle: –cross section where the center of the circle is the center of the sphere circumference of great circle: –circumference of the sphere hemisphere: –great circle divides a sphere into two halves

Theorem Surface Area of a Sphere –The surface area of a sphere is four times the product of π and the square of the radius of the sphere.

Example 1 Find the surface area of the sphere with diameter of 8 m. Leave your answer in terms of π.

Example 1a Find the surface area of a sphere with diameter of 14 inches. Give your answer in terms of π.

Example 2 Earth’s equator is about 24,902 miles long. Approximate the surface area of Earth.

Example 2A Find the surface area of a melon with circumference 18 inches. Round your answer to the nearest ten square inches.

Theorem Volume of a Sphere –The volume of a sphere is four thirds the product of π and the cube of the radius of the sphere.

Example 3 Find the volume of the sphere with radius 6 m. Leave your answer in terms of π.

Example 3a Find the volume to the nearest cubic inch of a sphere with diameter 60 inches.

Example 4 The volume of a sphere is 5000 cubic meters. What is the surface area of the sphere?

Example 4a The volume of a sphere is 4200 cubic feet. Find the surface area to the nearest tenth.

Homework