Any math geeks out there?

[Horus_Kol]

I was pondering a bit about spheres and spherical geometry the other day, and hit a problem...

basic maths says the circumference of a circle is twice the radius, multiplied by a constant pi

so: C = 2*pi*r

(sorry, HF is not geared up for math notation)..


anyway, then we get on to spheres...

the surface area of a sphere is generally given as:

SSA = 4*pi*r*r

but, i have a problem with this....


if you have a ring (circumference = 2*pi*r) and then rotate that ring about a diameter through pi, you describe a sphere... now, in my mind, that means that the SSA should be 2*pi*pi*r*r - so, why isn't it?

[coothead]

Hi there Stuart,

I am not as knowledgeable mathematically as you and cannot be thought of as a maths geek. :disagree:

As a sphere's surface area is generally accepted as being 4πr²,
then one must assume that your logic is flawed. :agree:

Basically you are applying the same logic that you would use to determine the surface area of a
cylinder by rotating a rectangle about its vertical axis.
For a curved surface it requires a different approach.

The value of r in the circumference of your circle is, obviously, constant

The value of r in the rotation of that circle to describe a sphere is not.

At the equator the value of r is, obviously r.

But as we approach the poles the value of r tends to zero.

Therefore 2πr x πr cannot produce the surface area of a sphere.

Q.E.D. ;)

[Pegasus]

http://www.teacherschoice.com.au/Maths_Library/Area%20and%20SA/area_2.htm

this explains it so *I* can understand it.