Question

A key lime pie in a 10.00 inch 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 108 inches. Express the angular distance that the pie plate has moved through in revolutions, radians, and degrees.(________) revolutions(________)radians(________)degreeIf the pie is cut into 9 equal slices, express the angular size of one slice in radians, as a fraction of pie?

Answer 1

The angular distance in revolution is
`revolution = 3.439 \ revolution`

The angular distance in radians is
`\theta_(rad)= 21.6 \ radians`

The angular distance in degrees is
`\theta =1238.04^o`

The angular size is
`Z = (2)/(9) \pi \ radians`

Step-by-step explanation:

From the question we are told that

The diameter is
`d = 10 \ inches`

The distance moved by the rim is
`D = 108 \ inches`

Generally the circumference of the pie plate is mathematically represented as

`C = \pi d`

Substituting the values

`C = 10 *3.142`

`= 31.42 \ inches`

The number resolution carried out by the pie plate is evaluated as

`revolution = (D)/(C)`

Substituting value

`revolution = (108)/(31.4)`

`revolution = 3.439 \ revolution`

The angular distance
`\theta_(rad)` is mathematically evaluated as

`\theta_(rad) = (D)/(r)`

Where r is the radius which is mathematically evaluated as

`r = (d)/(2) = (10)/(2) = 5 \ inches`

Substituting this into the equation for angular distance

`\theta_(rad) = (108)/(5)`

`\theta_(rad)= 21.6 \ radians`

The angular distance traveled in degrees is

`\theta = 3.439 *360`

`\theta =1238.04^o`

When the pie is cut into 9 equal parts

The angular size would be mathematically evaluated as

`Z = (2\pi)/(9)`

`Z = (2)/(9) \pi \ radians`