Volume of a Sphere

Objective: To solve problems involving volumes of spheres and hemispheres

Volume of a Sphere

TheoremTheorem: Sphere VolumeThe volume of a sphere with

radius r is V = ________.4/3 Π r3

V (sphere) = 4/3 Π r3

Volume of a Hemisphere

A hemisphere is _________ a sphere, so

V(hemisphere) = _______.

ALERT!

2/3 Π r3

one-half

Example: Finding Sphere Volume

EXAMPLE A Find the volume of a sphere that has

a radius of 6 inches.

V (sphere) = 4/3 Π r3

V (sphere) = ____________V (sphere) = ____________

Example: Using Sphere Volume to Find the Radius

EXAMPLE BFind the radius of a sphere that has a

volume of 2304 Π cubic centimeters.V (sphere) = 4/3 Π r3______= __________________= __________________= __________________= ____________

Final Checks for Understanding: Mixed Review

A plastic bowl is in the shape of a cylinder with a hemisphere cut out. The dimensions are shown. a. What is the volume of the cylinder?b. What is the volume of the hemisphere?c. What is the volume of plastic used to make the bowl?

An ice cream cone is 9 cm deep (height) and 4 cm across the top (diameter). A single scoop of ice cream, 4 cm in diameter, is placed on the cone. If the ice cream melts into the cone, will it overflow?

Final Checks for Understanding: Mixed

Review

Homework Assignment

Sphere Volumes WS