Why do you think cans are all much the same shape?  One factor is the cost.  Suppose the can is to have a volume of 375 cc.  Let it have radius r and height h.  If A is the area of the metal used in making the ends and the curved surface, you should be able to find A as a function of r ... .  Do this!

[Find A, V as functions of h and r; then eliminate h in the formula for A by writing it as a function of r and V (= 375). ]  

You should get

           
 1.3 Can do

 

We can see how this function
A(r) behaves by drawing the graph of the function.  
For r = 1, A =   6 + 750 = 756,
 for r = 2, A = 24 + 375 = 399, ... .
 









































Why do you think cans are all much the same shape? One factor is the cost. Suppose the can is to have a volume of 375 cc.  Let it have radius r and height h. If A is the area of the metal used in making the ends and the curved surface, you should be able to find A as a function of r ... . Do this!

[Find A, V as functions of h and r; then eliminate h in the formula for A by writing it as a function of r and V (= 375). ]  

You should get

   
 1.3 Can do

 

We can see how this function
A(r) behaves by drawing the graph of the function.

For r = 1, A = 6 + 750 = 756,
 for r = 2, A = 24 + 375 = 399, ... .
  
 

We might choose r = 4 cm.
A graph is a very useful way of picturing the behaviour of a function. In general,

The graph of a function f is the set of all points (x, f(x)) where x belongs to the domain of f.

Convention:  If f is given by a formula, we assume the domain of f to be the largest set of real numbers for which the definition makes sense.