Geometry

12.4 Spheres

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

3 rA 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

3 r

3)10(34

100034

3units 3

4000

2. area = 100π Volume: _____

Let’s try #2!

24 rSurface Area = Volume =34

3 r

3)5(34

Work backwards to find r!!

100π = 4πr2

25 = r2

r = 5125

34

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

3 r

3)41(

34

41

41

41

34

3units 481

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

34000 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 63√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 units³

HOMEWORK

pg. 500 CE #1-9 WE 1-23 odd