Question

Using spherical co-ordinate systems calculate the area of a disc of radius 2 cm.

Answer 1

Consider the circular disc with centre at origin of X-Y plane.
Circular disc is a part of cylinder in cylindrical system.
z = 0

Differential area = ds = rdrd Ф

s = ∫ds

`s = ∫_0^(2π) ∫_2^0 rdrdФ`
s = 2 x 2𝝅
s = 4 𝝅 m² 

Area of disc = 4𝝅 m²