Polygon β Cone
n-gon base area β Ο as n β β
Current sides
3
polygon
Ο estimate
-
error: -
Error
-
n = 3
Sides (n)
3
Animation
Volume of pyramid = (1/3) Γ base_area Γ height
base_area(n) = n Β· rΒ² Β· sin(2Ο/n) / 2 β n-gon, r=1
As n β β: base_area β Ο
base_area(n) = n Β· rΒ² Β· sin(2Ο/n) / 2 β n-gon, r=1
As n β β: base_area β Ο
Convergence Table
base area per number of sides
adjust the slider to begin
| Shape | Sides | Base area (β Ο) | Error |ΞΟ| |
|---|
Why does this give Ο?
The n-gon base has area nΒ·sin(2Ο/n)/2. As nββ,
sin(2Ο/n) β 2Ο/n, so area β n Β· (2Ο/n) / 2 = Ο.
The n-gon base has area nΒ·sin(2Ο/n)/2. As nββ,
sin(2Ο/n) β 2Ο/n, so area β n Β· (2Ο/n) / 2 = Ο.