Partial surface area of a sphere?

Assume the cone's axis coincides with the positive z-axis. Consider this "cap" of area cut off by the cone. Let φ denote the angle measured from the positive z-axis. Imagine a thin "ring" of the cutoff area generated by drawing a radius at some value of φ, changing φ by dφ (which draws a little piece of arc of length Rdφ), and sweeping that piece of arc around the sphere at constant φ. The radius of this ring is R sin(φ), and its area is

(R dφ)(2πR sin(φ)) = 2πR² sin(φ) dφ

Integrate this from φ=0 to φ=α where α is the generating angle of the cone. This gives the area of the "cap". You should get

2πR²(1 - cos(α))

This Site Might Help You.

RE:

Partial surface area of a sphere?

Lets say I have a sphere with a known radius R. If I take a cone section out of this sphere, such that the tip of the cone would be at the center of the sphere, the base of the cone would be a curved surface. If I know angle of this cone section (the angle at it's point), how can I find the...

use a spherical polar transformation and it shouldn't be that hard

you set one of the angles to 2pi and the other to whatever that angle of your cone is.

You would use the equation for the surface area of a sphere.

surface area = 4pi*r^2