Finding the maximum volume of a cylinder.The cylinder is open topped and is made from 200 cm 2 of material.So what I have done is said S = 2 π r 2 h + 2 π r 2 . 2 π r 2 h + 2 π r 2 = 200 2 π r 2 h = 200 − 2 π r 2 h = 200 − 2 π r 2 2 π r 2 Subbing this into the volume equation I get V = ( π r 2 ) 200 − 2 π r 2 2 π r 2 .Having trouble differentiating that equation.

Question

Finding the maximum volume of a cylinder.The cylinder is open topped and is made from   200         cm    2   of material.So what I have done is said   S  =  2  π      r    2    h  +  2  π      r    2  .                    2        π                  r          2                h        +        2        π                  r          2                                    =        200                            2        π                  r          2                h                            =        200        −        2        π                  r          2                                    h                            =                              200            −            2            π                          r              2                                            2            π                          r              2                                          Subbing this into the volume equation I get   V  =  (  π      r    2    )            200      −      2      π              r        2                    2      π              r        2            .Having trouble differentiating that equation.

cindysnifflesuz · Accepted Answer

Step 1Your equation for S is wrong. The lateral area is   2  π  r  h and the base area   π      r    2  , so S equals   2  π  r  h  +  π      r    2  .Following your steps, I get   V  =  (  π      r    2    )            200      −      π              r        2                    2      π      r        =  100  r  −      π    2        r    3  Step 2Summarized:       d          d      x            x    n    =  n      x          n      −      1      This means       d          d      r        V  =  100  −            3      π        2        r    2  I hope you can take it from there.

Finding the maximum volume of a cylinder. The cylinder is open topped and is made from 200cm^2 of material.

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