Volume of SpheresVolume of Spheres

Objective:Objective:1) To find the 1) To find the

volume of a sphere.volume of a sphere.

SpheresSpheres

Sphere Sphere – The set of all points in space – The set of all points in space equidistant from a given point.equidistant from a given point.

Center

r

Radius – Is a segment that has one endpt @ the center & the other endpt on the sphere.

Diameter – A segment passing through the center w/ both endpts on the sphere.

Volume of a sphereVolume of a sphere

Vs = (4/3)r3

Radius of a sphere

r

Ex.3: Find the volume of the Ex.3: Find the volume of the following sphere.following sphere.

30m

Vs = (4/3)r3

= (4/3)(15)3

= (4/3)(3375)= 4500= 14137m3

25 What is the volume of a sphere with a radius of 8 ft?

26 What is the volume of a sphere with a diameter of 4.25 in?

Find the volume of the sphere. Leave your answer in

terms of .

V = r 3 Use the formula for the volume of a sphere.43

302

= • 153 Substitute r = = 15.43

= 4500 Simplify.

The volume of the sphere is 4500 cm3.

Surface Areas and Volumes of Surface Areas and Volumes of SpheresSpheresLesson 11-6

Quick Check

Additional Examples

11-6

Finding Volume

2 cm

Volume of a Sphere(round to the nearest hundredths) 34

3

V r

V 3351. cm3

34 2

3V

10 cm

Volume of a Sphere

V 523 60. cm3

34

3V r

34 5

3V

5 in

Volume of a SphereA spherical balloon has an initial radius of 5 in. When more air is added, the radius becomes 10 in. Explain how the volume changes as the radius changes.

2 2523.6 in . 4,118.8 inV vs

10 in

34

3V r