Question

A sweet potato pie in a 10.00 in diameter plate is placed upon a rotating tray. Then, the tray is rotated such that the rim of the pie plate moves through a distance of 158 in. Express the angular distance that the pie plate has moved through in revolutions, radians, and degrees.

Answer 1

To express the angular distance of the pie plate, we need to find the circumference of the plate and calculate the angular distance using the given distance. The angular distance is 5 revolutions, 10 radians, and 1800 degrees.

Step-by-step explanation:

To express the angular distance that the pie plate has moved through in revolutions, radians, and degrees, we need to first find the circumference of the plate and then calculate the angular distance using the given distance.

Step 1: Find the circumference

The diameter of the plate is given as 10.00 inches, so the radius is half of that, which is 5.00 inches. The circumference of the plate is given by the formula C = 2πr, where r is the radius. Substituting the value, we get C = 2π * 5.00 = 31.4159 inches.

Step 2: Calculate the angular distance

The angular distance is defined as the ratio of the distance traveled to the circumference of the plate. Given that the distance traveled is 158 inches, the angular distance can be calculated as follows:

Angular distance (in revolutions) = Distance traveled / Circumference = 158 / 31.4159 = 5 revolutions.

Angular distance (in radians) = 2π * Angular distance (in revolutions) = 2π * 5 = 10π radians.

Angular distance (in degrees) = 360 * Angular distance (in revolutions) = 360 * 5 = 1800 degrees.