Explanation:
It is given that,
Diameter of the peach pie, d = 9 inches
Radius of the pie, r = 4.5 inches
The tray is rotated such that the rim of the pie plate moves through a distance of 183 inches, d = 183 inches
Let
is the angular distance that the pie plate has moved through.
It is given by :


Since, 1 radian = 57.29 degrees

Since, 1 radian = 0.159155 revolution

Hence, this is the required solution.
The work done to pull the sister back on the swing is equal to the increase in potential energy of the sister:

(1)
where m is the sister's mass, g is the gravitational acceleration and

is the increase in altitude of the sister with respect to its initial position.
By calling

the angle of the chain with respect to the vertical, the increase in altitude is given by

(2)
where L is the length of the chain.
Putting (2) inside (1), we find

from which we can find the mass of the sister:
Answer:
Sundial is an instrument showing the time by the shadow of a pointer cast by the sun on to a plate marked with the hours of the day.