Derive a generalized expression of surface area of right cir

Derive a generalized expression of surface area of right circular cylinders of constant volume normalized to the volume of a sphere. What does the graph look like?

Solution

Let the constant volume of right circular cylinder be v

Volume of cylinder = r² h=v

Surface area of cylinder= (2rh+2r²)

We can write the above equation as (2r²h/r + 2v/h)

=2v/r + 2v/h

As cylinder volume is normalized to sphere volume which means sphere is enclosing cylinder

=> (R²)=(r² + (h/2)²) where R is radius of sphere