Answer to Question #299620 in Molecular Physics | Thermodynamics for phys

Question

Consider a sphere of radius R. It is a three-dimensional shape that is bounded by its surface area, a two-dimensional shape. The mathematical equation for the sphere is:

R2 = x² + y² + z². Write the expression for volume (enclosed quantity) and the surface (bounding quantity) of this sphere.

Answer 1

three dimensional sphere

Radius

$R=\sqrt{x^2+y^2+z^2}$

Area

$A=\pi R^2$