Question

Please help...This is all one question.
Many Common formulas from geometry can now be proven using integration. How would you prove the volume of a sphere of radius r is V = 4/3πr3? How would you prove the volume of a right-circular cone of radius r and height h is V = 1/3 πr3 h ? What is the Volume of an ellipse with minor axis 2a, and major axis 2b (where a < b), revolved about its major axis? This is called a prolate ellipsoid). Prove it.

Answer 1

for V = 4/3πr3?

you can integrate using the equation of a sphere

it ill be a triple integral Using spherical coordinates.