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

Answer:

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   $Z = \frac{2}{9} \pi \ radians$

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

           $revolution = \frac{D}{C}$

Substituting value

            $revolution = \frac{108}{31.4}$

                              $revolution = 3.439 \ revolution$

The angular  distance $\theta_{rad}$ is mathematically evaluated as

                $\theta_{rad} = \frac{D}{r}$

             Where r is the radius which is mathematically evaluated as

                        $r = \frac{d}{2} = \frac{10}{2} = 5 \ inches$

Substituting  this into the equation for angular distance

                      $\theta_{rad} = \frac{108}{5}$

                              $\theta_{rad}= 21.6 \ radians$

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

                         $Z = \frac{2\pi}{9}$

                           $Z = \frac{2}{9} \pi \ radians$