# CONSTANT AREA

FORMULAS:Circumference =

Volume of a Cylinder =

Consider the area of the two rectangles.(93.5 in2).Think of making baseless cylinders from all the rectangles with an area of 93.5 in2.Can you find the dimensions of the rectangle that would produce the cylinder with the greatest volume?

PREDICT:Do you think the shorter-wider cylinder or the tall-narrow cylinder will have 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 5.5 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?__________

Suggest another rectangle that is not on the chart that you think might have a greater volume and calculate its volume.

Would you ever find the absolute biggest volume?__________

Does the function achieve a maximum value?__________

Explain the behavior of the graph as r gets smaller.