Multiple Integrals - Volume of a drilled space in a sphere

I have enclosed all details on the attached file. How do I find the volume of the drilled area? Consider a sphere of radius R and circular hole 2d drilled through along axis of symmetry...

Multiple Integrals - Volume of a sphere

Please find details on the attached file. Thank you

It is the problem of finding the differential equation of all parabolas whose axes are parallel to the axis of y.

Differential Equation (XII) Formation of Differential Equations by Elimination It is the problem of finding the differential equation of all parabolas whose axes are parallel to the axis of y.

To prove that function f(x,y)=xy(x+y)

iIgave the difinition that a function f of two variables is differentiable at (a,b) My definition goes: if the function has its derivatives at point (a,b) then the function is differentible at (a,b) How to prove on the base of the definition, the function f defined by f(x,y)=xy(x+y) is differentiable at every point of its domain.

I have no idea of going about this proof

g(x,y)=｜x｜y (that's module sign) prove that g is not differentiable at (0,b) for any value non-zero value of b