To model the number of cups of juice needed to fill a semi-spherical bowl with a radius of 'r' inches, we first need to find the volume of the bowl.
The volume of a sphere is given by the formula:
V = (4/3)πr³
Since we are dealing with a semi-sphere, we divide the volume by 2:
V = (2/3)πr³
Now, we can convert the volume to the number of cups needed by dividing it by the volume of each cup of juice (approximately 14 cubic inches):
Cups = V/14
Therefore, the general equation to model the number of cups of juice needed to fill a semi-spherical bowl with a radius of 'r' inches is:
Cups = [(2/3)πr³]/14