How do you find the surface area generated when the curve #y=sqrt(r^2-x^2), 0<=x<=a# is rotated about the x axis?
Take a piece of the curve whose length is the differential of arc length
The surface area of the corresponding piece of the solid is
the circumference of revolution time the differential of arc length
Using just the values
# = 2pi int_0^a r dx#
# = 2pi r a#
The formular is