FORMULAS:Circumference = 

Volume of a Cylinder = 

Consider the perimeter of the two rectangles.(39 in).Think of making baseless cylinders from all the rectangles with a perimeter of 39 in.Can you find the dimensions of the rectangle that would produce the cylinder with the greatest volume?

PREDICT:What is the height of the cylinder that has the largest volume?

SOLVE: Complete the table.(You can use your graphing calculator to generate this table.Show me what you enter in LISTS, or the Y= screen.)
Height of Rectangle (in.)
Width of Rectangle (in.)
Radius of 

Cylinder (in.)

Volume of Cylinder (in.3)















Of all the rectangles on the chart, which gives the cylinder with the greatest volume?__________

Do you think that would be the largest on possible?__________

Make a graph from the chart with the volume on the y axis and the height on the x axis.Indicate with a star the point on your graph that represents the greatest volume.

Write an expression for the volume of the cylinder as a function of its radius.(hint:Use the two formulas provided.).Graph the expression, using your graphing calculator.Where does the function achieve its maximum value?