x volume and surface area of a sphere
V =^43 ʌU^3.
total surface area = 4ʌU^2.
ͼ6HH)LJXUHͽ
Summary
,QWKUHHGLPHQVLRQDOVSDFH¿JXUHVDUHFDOOHGVROLGV,QWKLVOHVVRQZHUHYLHZWKHQDPHVRIFODVVLF
three-dimensional shapes and develop formulas for their surface areas and volumes.
([DPSOH
Derive a formula for the surface area of a right circular cylinder with height h and
base radius rͼ6HH)LJXUHͽ
6ROXWLRQ
We can image a cylinder as constructed by rolling a rectangular
SLHFHRISDSHULQWRWKHVKDSHRIDWXEHͼDQGWKHQDWWDFKLQJFLUFXODU
GLVFVDWHDFKHQGͽ7KLVUHFWDQJOHKDVOHQJWKʌUDQGKHLJKWh.
ͼ6HH)LJXUHͽ
7KHODWHUDODUHDRIWKHF\OLQGHULVWKXVʌUh, and its total surface area is
222.SSS S Srh r^22 r rh r^2
([DPSOH
A cone has a regular hexagon with side length 6 inches for its base. Each lateral edge of the cone has length
10 inches.
Dͽ :KDWLVWKHVODQWKHLJKWRIHDFKIDFHRIWKHFRQH"
Eͽ :KDWLVWKHODWHUDODUHDRIWKHFRQH"
Fͽ :KDWLVWKHWRWDOVXUIDFHDUHDRIWKHFRQH"
Gͽ :KDWLVWKHKHLJKWRIWKHFRQH"
Hͽ :KDWLVWKHYROXPHRIWKHFRQH"
r
Figure 23.7
Figure 23.8
r
h
r
hh
2 Sr
Figure 23.9