ADVANCED EXERCISES

(3)
 (a) Given a one-litre cylinder can, express its surface area as a 
     function of its radius.

 (b) Given a cylinder can of volume V, express its surface area as a 
     function of its radius.

 (a) Surface Area = 2(r2) + 2rh
           Volume = r2h = 1000
                 ==>  h = 1000/(r2)

     Surface Area = 2r2 + 2r(1000/(r2))
                  = 2r2 + 2000/r

 (b) Surface Area = 2r2 + 2rh
           Volume = V =r2h
                           V
                  ==> h = ----
                           r2

                               V
     Surface Area = 2r2 + 2r----
                               r2

                           2V
                  = 2r2 + ---
                            r

The Surface Area given in terms of the radius is 2r2 + 2V/r.