Question

A cherry pie in a 10.50 in diameter plate is placed upon a rotating tray. The tray is rotated such that the rim of the pie plate moves through a distance of 258 in. Express the angular distance that the pie plate has moved through in revolutions, radians, and degrees. If the pie is cut into 11 equal slices, express the angular size of one slice in radians, as a fraction of pi?

Answer 1

The angular distance that the pie plate has moved through is approximately 49.14 radians, 7.82 revolutions, and 2815.2 degrees. The angular size of one slice of the pie is approximately 4.47 radians or 1.42π.

Step-by-step explanation:

To find the angular distance that the pie plate has moved through, we can use the formula:

angle (in radians) = distance traveled / radius of the plate

Given that the distance traveled is 258 inches and the radius of the plate is 5.25 inches (half of the diameter), we can substitute these values in to calculate the angular distance.

angle (in radians) = 258 inches / 5.25 inches = 49.14 radians