- #1
rohanprabhu
- 414
- 2
I was trying my hand at integrals with 2 variables... So.. my first excercise was to find out the surface area of a sphere. So, the co-ordinate system is something like this:
i] The whole co-ordinate system is mapped on the surface of a sphere.
ii] The x-axis of the sphere is like the equator of the earth.
iii] The y-axis of the sphere is like the prime meredian of the earth.
So, for the area, I used:
[tex]
A = \int^{2\pi r}_{0}dx\int^{2\pi r}_{0}dy
[/tex]
giving me the area:
[tex]
A = 4 \pi^2 r^2
[/tex]
Which is ofcourse wrong.. because if i look from the first equation, it is more like I'm calculating the area of a square lamina having lengths [itex]2 \pi r[/itex] each.
i] The whole co-ordinate system is mapped on the surface of a sphere.
ii] The x-axis of the sphere is like the equator of the earth.
iii] The y-axis of the sphere is like the prime meredian of the earth.
So, for the area, I used:
[tex]
A = \int^{2\pi r}_{0}dx\int^{2\pi r}_{0}dy
[/tex]
giving me the area:
[tex]
A = 4 \pi^2 r^2
[/tex]
Which is ofcourse wrong.. because if i look from the first equation, it is more like I'm calculating the area of a square lamina having lengths [itex]2 \pi r[/itex] each.