# CONSTANT PERIMETER

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) 1 2.5 5 6.5 8.5 10 11

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?