Question

A key lime 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 208 in. Express the angular distance that the pie plate has moved through in revolutions, radians, and degrees. A) Find the angular distance in revolutions, radians and degrees. B)If the pie is cut into 5 equal slices, express the angular size of one slice in radians, as a fraction of .

Answer 1

Answer:

A

  The distance in revolutions is $n = 7 \ revolutions$

    The distance in degrees  is  $\theta =2529 ^ o$

   The distance in radian is  $\theta_{radian } = 44.15 \ rad$

B

  $\theta_a = 1.26 \ rad$

Explanation:

From the question we are told that

  The diameter of the pie is  $d = 10.00 \ in$

  The distance covered by the rim  is  $D = 208 \ in$

   The number which the pie is divided into  is  k = 5

Generally the radius of the pie is mathematically represented as

      $r = \frac{d}{2}$

=>  $r = \frac{10}{2}$

=>  $r = 5 \ in$

Generally the distance covered by the rim is mathematically represented as

    $D= 2 \pi r n$

=>  $208 = 2* 3.142 * 5 * n$

=> $n = 7 \ revolutions$

Generally converting to  degrees

     $\theta = n * 360$

=>  $\theta = 7 * 360$

=>  $\theta =2529 ^ o$

Generally converting to  radian

   $\theta_{radian } = \frac{\theta * \pi}{180 }$

=>$\theta_{radian } = \frac{2520 * 3.142 }{180}$

=>$\theta_{radian } = 44.15 \ rad$

Generally the angular size of one piece of the pie is  

      $\theta_a = \frac{2 * \pi }{ k}$

=> $\theta_a = \frac{2 * 3.142}{ 5}$

=> $\theta_a = 1.26 \ rad$