Area of a spherical surface

Gurgle

Hi All,

This is wrecking my head.
Area of a sphere is 4 x pi x r2, grand no problem there.
If you slice off a section of the sphere, how do you calculate the area of the section?

e.g. sphere of 10mm radius has a surface area of 1256mm2, if you cut a 'disk' off with a radius of 5mm, whats the surface area of that piece?

ant.lei

Hello, I think you will need to use calculus to find it. A sphere is obtained by rotating a semi-circle about its diameter. Your 'disk' can be obtained in the same way, with only part of the semi-circle. Does it sound plausible to you?

If you are convinced by that, you can use the formula for area of surface of resvolution to find the area. See the link below.
http://en.wikipedia.org/wiki/Surface_of_revolution

Gurgle

ant.lei wrote:

Hello, I think you will need to use calculus to find it.

Thanks, but luckily I avoided calculus

Wikipedia to the rescue:
http://en.wikipedia.org/wiki/Spherical_cap

2 x pi x r x h

phew!
What I was missing was the phrase 'spherical cap'.

ant.lei

Sorry for scaring you with calculus. I didn't know there is such a simple formula for that. Cheers for pointing it out.