SOLUTION: A rectangular piece of sheet metal with an area of 800 in2 is to be bent into a cylindrical length of stovepipe having a volume of 400 in3. What are the dimensions of the sheet met

Let the dimensions of the rectangular piece be x and y,

    where y be the height of the cylinder.

    (Hence, x is the dimension to be bent into circle/cylinder).


Then we have  FIRST EQUATION  for the original area of the piece 

    xy = 800     (1)     (square inches)


When the dimension "x" is bent to the circle (to the cylinder latent surface), its radius becomes  r = .


Then the volume of the cylinder is  

    V =  =  =  =    cubic inches,


therefore our  SECOND EQUATION is

     = 400,     (2)       

or

      = .     (2').


Thus we have the system of two equations


     xy = 800,          (1)

      = .    (2')


In  (2')  replace  xy  by  800,  based on (1).  You will get

      = ,    or

     x = .


Thus you solved for x.  Now substitute  x =   into (1) to get

      = 800.


Then you get  y =  = .


Answer.   x =  inches;   y =  inches.