1. A cylinder of length 2x is inscribed in a sphere of radius a. Between one end of this cylinder and the sphere, another cylinder of length 2y is inscribed with one end on an end of the first cylinder so that the axes of the cylinder are collinear.
Show that the sum of the volumes of the two cylinders is

V=2Pi(x+y)(a^2-X^2-4y^2)

Question

1.	 A cylinder of length 2x is inscribed in a sphere of radius a. Between one end of this cylinder and the sphere, another cylinder  of length 2y is inscribed with one end on an end of the first cylinder so that the axes of the cylinder are collinear.
   Show that the sum of the volumes of the two cylinders is 
                               
    V=2Pi(x+y)(a^2-X^2-4y^2)

anonymous · Answer

anybody pls help

anonymous · Answer

attachment

phi · Answer

attachment

anonymous · Answer

Hi Phi .. Thanks a lot..

phi · Answer

I notice I have a typo in the second to last line, but I assume you can fix it

anonymous · Answer

Hi phi, will u help me to solve some of this probs .. ?/ Thanks..

phi · Answer

Did you make any progress?

The first problem is known as a Bernoulli Equation, of the form
y' + P(x) y = Q(x) y^n

phi · Answer

multiply through by (1-n) y^(-n)