Geometry 12.4 Spheres

Surface Area Formula Surface 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 = A way to remember which formula is cubed… The volume formula has two 3’s and volume is measured in units 3 !!

1. radius = 10 Area: _____ Volume: _____ Try this one! Surface Area = = 4π(10) 2 = 4 π (100) = 400π units 2 Volume =

2. area = 100π Volume: _____ Let’s try #2! Surface Area = Volume = Work backwards to find r!! 100π = 4πr 2 25 = r 2 r = 5

3. radius = ¼ Area: _____ Volume: _____ Try this one! Surface Area = = 4π(1/4) 2 = 4 π (1/16) = ¼ π units 2 Volume =

Push your desks together and solve #1-5!!! Change #3 (400 to 4000)

1. radius = Surface Area: _____ Volume: _____ 2. Area = 576 π Radius: _____ Volume: _____ 3. Volume = Radius: _____ Surface Area: _____ 12π units 2 4√3π units π units π units 2

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 Area of the blue circle = 27π cm 2 Volume = cylinder volume + ½ (sphere volume) = πr 2 h + ½ (4/3 πr 3 ) = π ½ (4/3 π3 3 ) = 90π + 18π = 108π units ³

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