A machine drill removes a core from any cylinder. Suppose you want the amount of material left after the core is removed to remain constant. The table below compares the height and radius needed if the volume of the hollow cylinder is to remain constant.

a. Plot the data points, (x, h), and draw a smooth curve through them.
b. Explain what happens to the height of the figure as the radius gets smaller. How small can x be?
c. Write a formula for the volume of the hollow cylinder, V, in terms of x and h.
d. Solve the formula in 13c for h to get a function that describes the height as a function of the radius.
e. What is the constant volume?

2.5 3.0 3.54.04.5 5.0 5.5 6.0 6.5 Height 56.6 | 25.5 | 15.4| 10.6 | 7.8 6.1 | 4.9 | 4.0 | 3.3