Surface Area of a Sphere

[Jon G.]

This solution may seem trivial, since it's already been done, but for those
interested, this page shows the calculus for deriving the surface area of a
sphere.

http://mypeoplepc.com/members/jon8338/math/id17.html


Jon Giffen
***@peoplepc.com

[hostlocal]

Post by Jon G.
This solution may seem trivial, since it's already been done, but for
those interested, this page shows the calculus for deriving the surface
area of a sphere.
http://mypeoplepc.com/members/jon8338/math/id17.html
Jon Giffen

you need to show all the steps.

[Jon G.]

">

Post by hostlocal
you need to show all the steps.

Suppose a sphere with center located at the origin is sliced by a plane
parallel with the xz axis. This forms a circle. The xy plane slices the
circle at a point in Quadrant I. The angle between this point, the origin
and the x axis is angle w.

Angle w = (Arclength A)/(radius r)

w = A/r

wr = A differentiating,

rdw + wdr = dA The radius doesn't change, so dr=0

rdw = dA

C is the circumference of the parallels at each increment of dA. Each
parallel has a radius of r cos w. A band of surface area dS of
Circumference C is,

dS=CdA

dS=2pi r cos w dA

dS=2pin r^2 cos w dw

Integrating from w= -pi/2 to pi/2,

S = 4pi r^2

http://mypeoplepc.com/members/jon8338/math/id17.html

has a diagram to facilitate this spoon-feeding.