PlanetMath: area of spherical calotte by means of chord

(more info)

Math for the people, by the people.

Main Menu

area of spherical calotte by means of chord

(Derivation)

Let the arc of a circle with radius rotate about the diameter . The surface of revolution is a spherical calotte with the height . If the length of the chord is , we obtain from the right triangle the proportion equation

$\displaystyle \frac{h}{k} = \frac{k}{2r},$

i.e. the chord

is the central proportional of the height and the diameter. Accordingly, we can substitute

$\displaystyle A = 2\pi rh$

of the area of the spherical calotte derived in the parent entry. Thus we have an alternative formula

$\displaystyle A = \pi{k}^2$

(1)

for finding the area of a spherical calotte.

Bibliography

1: K. V¨AISÄLÄ: Geometria. Kymmenennen painoksen muuttamaton lisäpainos. Werner Söderström Osakeyhtiö, Porvoo & Helsinki (1971).

"area of spherical calotte by means of chord" is owned by pahio.

(view preamble)

Other names:

alternative way to find area of spherical calotte

Keywords:

spherical calotte

This object's parent.

Log in to rate this entry.
(view current ratings)

51M04 (Geometry :: Real and complex geometry :: Elementary problems in Euclidean geometries)

Pending Errata and Addenda

None.

Discussion

forum policy

No messages.

Interact