Question: 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

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.

d X d 0 4.2 6 5.8 1 3.8 7 5.4 2

(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).

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

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