A draftsman is asked to determine the amount of material required to produce a machine part (see figure). The diameters d of the part at equally spaced points x are listed in the table. The measurements are listed in centimeters.

(a) Use these data with Simpson’s Rule to approximate the volume of the part.
(b) Use the regression capabilities of a graphing utility to find a fourth-degree polynomial through the points representing the radius of the solid. Plot the data and graph the model.
(c) Use a graphing utility to approximate the definite integral yielding the volume of the part. Compare the result with the answer to part (a).

Transcribed Image Text:

d X d 0 4.2 6 5.8 1 3.8 7 5.4 2 4.2 8 4.9 3 4.7 9 4.4 4 5 5.2 5.7 10 4.6