Question

Compute the surface area of the sphere S : (x ^ 2) + y ^ 2 + z ^ 2 = a ^ 2 using surface integral.

Answer 1

Step-by-step explanation:

How would you calculate the surface area of the portion of the sphere x2+y2+z2=16zx2+y2+z2=16z that lies within the paraboloid z=x2+y2z=x2+y2.

Points common to the sphere and paraboloid satisfy the equation z+z2=16zz+z2=16z, so there we have either z = 0 or z = 15. The former corresponds to the origin (0, 0, 0) which lies in both surfaces where they both have z = 0 as a tangent plane.

However I am not sure how to continue. Could anyone please guide me through how you would attempt this question? thank you