Help. A CONE, SPHERE, and CYLINDER have equal radii and heights.
Use algebra and the Volume formulas to show that the volume of the cylinder is equal to the volume of the cone
PLUS the volume of the Sphere.

Step-by-step explanation:

Prove this:

volume of cylinder = volume of cone + volume of sphere

       πr²h                 = (1/3)πr²h              +  (4/3)πr³

Note that the factor πr² is common to all three of these formulas.  Factoring out this πr², we get:

           h                     = h/3                      + (4/3)r

or:        3h/3                = h/3                       + 4r/3

or:          3h                   = h                         + 4r

or:            2h                   =                        4r

or:               h                    =                 2r

Note that 2r is the diameter of the sphere, and that this diameter is twice the radius.  Thus, in view of the givens. this equation h = 2r is correct.

Thus, the volume of the cylinder is equal to the volume of the cone  PLUS the volume of the sphere.

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