Answer:
The angular distance in revolution is [tex]revolution = 3.439 \ revolution[/tex]
The angular distance in radians is [tex]\theta_{rad}= 21.6 \ radians[/tex]
The angular distance in degrees is [tex]\theta =1238.04^o[/tex]
The angular size is [tex]Z = \frac{2}{9} \pi \ radians[/tex]
Explanation:
From the question we are told that
The diameter is [tex]d = 10 \ inches[/tex]
The distance moved by the rim is [tex]D = 108 \ inches[/tex]
Generally the circumference of the pie plate is mathematically represented as
[tex]C = \pi d[/tex]
Substituting the values
[tex]C = 10 *3.142[/tex]
[tex]= 31.42 \ inches[/tex]
The number resolution carried out by the pie plate is evaluated as
[tex]revolution = \frac{D}{C}[/tex]
Substituting value
[tex]revolution = \frac{108}{31.4}[/tex]
[tex]revolution = 3.439 \ revolution[/tex]
The angular distance [tex]\theta_{rad}[/tex] is mathematically evaluated as
[tex]\theta_{rad} = \frac{D}{r}[/tex]
Where r is the radius which is mathematically evaluated as
[tex]r = \frac{d}{2} = \frac{10}{2} = 5 \ inches[/tex]
Substituting this into the equation for angular distance
[tex]\theta_{rad} = \frac{108}{5}[/tex]
[tex]\theta_{rad}= 21.6 \ radians[/tex]
The angular distance traveled in degrees is
[tex]\theta = 3.439 *360[/tex]
[tex]\theta =1238.04^o[/tex]
When the pie is cut into 9 equal parts
The angular size would be mathematically evaluated as
[tex]Z = \frac{2\pi}{9}[/tex]
[tex]Z = \frac{2}{9} \pi \ radians[/tex]
