Calculate the area of the circle by the indicated method.
The lengths of parallel chords of a circle that are 0.250 in. apart are given in the following table. The diameter of the circle is 2.000 in. The distance shown is the distance from one end of a diameter.

Using the formula A = πr² , the area of the circle is 3.14 in.².

Find the area of the circle using Simpson’s rule and the same table values as in Exercise 19. Explain why the value found is closer to 3.14 in.2 than the value found in Exercise 19.

Data from Exercises 19

Find the area of the circle using the trapezoidal rule and only the values of distance of 0.000 in., 0.500 in., 1.000 in., 1.500 in., and 2.000 in. with the corresponding values of the chord lengths. Explain why the value found is less than 3.14 in.² .

Transcribed Image Text:

Distance (in.) 0.000 0.250 0.500 0.750 1.000 1.250 1.500 1.750 2.000 Length (in.) 0.000 1.323 1.732 1.936 2.000 1.936 1.732 1.323 0.000