Pretty much the title, Cannot fathom why titled formula is invalid or not in use?
We take half the vertical cirucmference, pi * r and rotate it around the horizontal periphery on its axis, 2 * pi * r, this should give the value of surface area.
Pic just for reference –
https://qphs.fs.quoracdn.net/main-qimg-902ca0ec6c07471c700357a711f7e70c-c
In: Mathematics
Let’s imagine a point on that vertical half-circumference. First, let’s imagine the point is on the equator. When we rotate it around the vertical axis, it does indeed travel the circumference 2*pi*r. But what if we imagine the point is close to the pole? When we rotate it around the vertical axis, it travels in a much smaller circle, much less than 2*pi*r. So, that part contributes much less to the total surface area. Your formula works only if the horizontal distance from the vertical axis to the surface is the same everywhere, which is true for a cylinder, not a sphere.
>around the horizontal periphery on its axis, 2 * pi * r
That is only the distance it is rotating at its equator, not everywhere. Every point is going a different distance. What you are describing is a cylinder, no a sphere.
Because you can’t just multiply those two values as if the sphere was a square with those side lengths. The shape isn’t flat so when you rotate it around you don’t multiply the values, you need to do integration to find the volume of the solid of revolution. If you do this for the limits of a sphere then you get the formula 4*πr^*2.
Take a look here for a more in depth explanation of the maths. [https://brilliant.org/wiki/surface-area-sphere/](https://brilliant.org/wiki/surface-area-sphere/)
Latest Answers