Geometry

12.4 Spheres

• Please add sphere to your vocab list

Surface Area Formula24 rSurface Area =

Does this seem accurate?

Let’s investigate.

r

What does this represent?

Does it seem like 4 of these blue circles would cover the sphere?The formula says “Yes!”

It represents the area of a circle with radius = r.

Volume Formula

Volume =34

3r

A way to remember which formula is cubed…The volume formula has two 3’s and volume is measured in units3!!

1. radius = 10 Area: _____ Volume: _____

Try this one!

24 rSurface Area =

= 4π(10)2

= 4π(100)

= 400π units2

Volume =34

3r

3)10(3

4

10003

4

3units 3

4000

2. area = 100π Volume: _____

Let’s try #2!

24 rSurface Area = Volume =34

3r

3)5(3

4

Work backwards to find r!!

100π = 4πr2

25 = r2

r = 5

1253

4

3units 3

500

3. radius = ¼ Area: _____ Volume: _____

Try this one!

24 rSurface Area =

= 4π(1/4)2

= 4π(1/16)

= ¼ π units2

Volume =34

3r

3)4

1(

3

4

4

1

4

1

4

1

3

4

3units 48

1

Push your desks together and solve #1-5!!!

Change #3 (400 to 4000)

31. radius = Surface Area: _____ Volume: _____

2. Area = 576π Radius: _____ Volume: _____

3. Volume = Radius: _____ Surface Area: _____

12π units2 4√3π units3

12 2304π units3

3

4000 10 400π units2

3

10

4. Find the area of a circle formed when a plane passes 3 cm from the center of a sphere with radius 6 cm.

5. Find the volume of the given structure.

3 6

3√3Area of the blue circle = 27π cm2

Volume = cylinder volume + ½ (sphere volume) = πr2h + ½ (4/3 πr3) = π3210 + ½ (4/3 π33)

= 90π + 18π

= 108π units2

HW

• P. 500-501 CE (CE 7-9 all, WE 1-25 odd)

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