Right Cone Volume and Area
Right Cone Volume and Area
Let be a circle of radius and center . A right cone with base and apex directly above is the surface formed by joining all the points of to .
B
r
C
B
P
C
B
P
The volume of the cone is , where is the height and is the area , , so that .
V=hb
1
3
h
b
B
b=π
2
r
V=πh
1
3
2
r
The volume was determined by several ancient Greek mathematicians, including Eudoxus, Archimedes and Euclid.
The surface area has two parts, the base and the lateral surface area , which is , where is the slant height , using the Pythagorean theorem.
b
S
S=πrs
s
s=+
2
h
2
r