Volume of a Cylinder =
Consider the area of the two rectangles.(93.5 in^{2}).Think of making baseless cylinders from all the rectangles with an area of 93.5 in^{2}.Can you find the dimensions of the rectangle that would produce the cylinder with the greatest volume?
PREDICT:Do you think the shorterwider cylinder or the tallnarrow 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.)


Cylinder (in.) 

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.