This document provides formulas and examples for calculating the surface area and volume of spheres and hemispheres. It defines key terms like sphere, great circle, and hemisphere. Formulas are given for the surface area and volume of full spheres and hemispheres. Examples show how to use the formulas to find the surface area and volume of spheres with given radii or diameters.

1. Obj. 53 Spheres
The student is able to (I can):
• Find the surface area and volume of spheres and
hemispheres

2. 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

3. Formulas Sphere:
Hemisphere:
(a sphere has no lateral area)
= π 34
V r
3
r
= π 2
S 4 r
= π 32
V r
3
= π 2
S 3 r
(if closed)

4. Examples Find the surface area and volume:
1. A sphere with radius 9 m.
2. A hemisphere with radius 12 ft.
( )2 2
S 4 9 324 m= π = π
( )3 34
V 9 972 m
3
= π = π
( )2 2 21
S 4 r r 3 r
2
= π + π = π
( )2 2
3 12 432 ft= π = π
( )3 32
V 12 1152 ft
3
= π = π

5. 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 2
S 4 10 400 in= π = π
( )3 34 4000
V 10 in
3 3
= π = π
34
r 7776
3
π = π
( )3 3
r 7776 5832
4
 = = 
 
3
r 5832 18 ft.= =