Volume of a Cylinder
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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.)


Cylinder (in.) 

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?