Warm Up

Give the formulas for the volume of the following figures

Cylinder:__________________Prism:__________________

Pyramid:__________________Cone:___________________

Today’s Lesson: Volume of Spheres

March 31, 2014

What is a Sphere?

• A sphere is a set of all point in space equidistant from a given point called the center.

• This sounds just like the definition of a circle.

• What differences do you notice about the sphere(to the left) and a regular circle?

r

Radius of a Sphere

Just like a circle a Sphere

has a radius and a diameter

as well!!!!

So what can we say about the diameter?

A radius is a segment that

has one endpoint at the center and the other endpoint on the sphere.

If you cut a sphere right down the middle you would create two congruent halves called HEMISPHERES.

You can think of the globe. The equator cuts the earth into the northern and southern

hemisphere.Which

hemisphere do we live on?

Look at the cross section formed when you cut a sphere in half.

What shape is it?

A circle!!! This is called the GREAT CIRCLE of the sphere.

This is where the diameter and the radius are located.

Unlike circles the diameter and radius have to go through a particular part of the sphere.

Volume of a Sphere

34

3V r

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

You Try!!!

Find the volume of the

following figures.

7 cm 25 m

V ≈ 1436.8 V ≈ 8181.2

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

Did I hear someone say this is easy?

Well let’s take it up a notch!!!!!!!!!

? cm

Find the radiusV

r

( )4

3

3

3(4 r )33.51

3

V 3351. cm3

3(4 r )3 33.51x

3100.53r

4

38 r2 r

? cm

Find the diameterV

r

( )4

3

3

3(500 ) (4 r )

3 3

3(500 ) cm

3V

3(4 r )500

3500r

4

3125 r5 r 10 d

You Try!!!!

Find the radius if the volume of the sphere is 904.78 .

? cm

r ≈ 6 cm

You Try!!!!

Find the diameter if the volume of the sphere is 7238.23 .

? cm

d ≈ 24 cm

What about finding the volume of a hemisphere?

Formula: A hemisphere is

half of a sphere so just take half of the formula for volume

of a sphere.

Now let’s make things a little more

challenging!!!!!!!!!

Finding the volume of composite Figures!!!!

Finding the volume of composite Figures!!!!

Finding the volume of composite Figures!!!!

You Try!!!!