Obj. 53 Spheres

The student is able to (I can):

• Find the surface area and volume of spheres and hemispheres

sphere

great circle

hemisphere

The set of all points in space that are a fixed distance from a given point

The intersection of a plane and a sphere, including the center of the sphere.

Half of a sphere, created by a great circle

Formulas Sphere:

Hemisphere:

(a sphere has no lateral area)

= π34

V r3

r

= π2S 4 r

= π32

V r3

= π2S 3 r

(if closed)

Examples Find the surface area and volume:

1. A sphere with radius 9 m.

2. A hemisphere with radius 12 ft.

( )2 2S 4 9 324 m= π = π

( )3 34V 9 972 m

3= π = π

( )2 2 21S 4 r r 3 r

2= π + π = π

( )2 23 12 432 ft= π = π

( )3 32V 12 1152 ft

3= π = π

3. A sphere with diameter 20 in.

r = 10 in.

4. What is the radius of a sphere whose volume is 7776π cubic feet.

( )2 2S 4 10 400 in= π = π

( )3 34 4000V 10 in

3 3= π = π

34r 7776

3π = π

( )3 3r 7776 5832

4

= =

3r 5832 18 ft.= =