Assignment 9 — problem solving
Due Friday, February 2
- As always, it is strongly recommended that you carefully read the entire assignment before attempting to produce your solution.
- Based upon hours of research, zillions of jelly beans, and a bunch of mason jars, it has been concluded that the volume of a jelly bean can be roughly modeled as the average of the volume of the exterior bounding cylinder and of the volume of the interior bounding ellipsoid.
- Our formula for the volume j of a single jelly bean is:
where a and b are respectively the length and height of the jelly bean.
- Exhaustive research has determined the loading factor — the percentage of a jar that can be occupied by jelly beans — is constant, with the constant being 69.8% (i.e., .698).
- Your task is to produce a program that separately prompts and reads three values, their order being the average length and height of a jelly bean (decimal values), and the size of a jar (integer value). The dimensions are in centimeters and the volume of the jar is in mLs (note: one mL equals one cubic centimeter).
- The estimate for the number of beans that can fit in the jar is
v F / j
where v, F, and j are respectively the volume of the jar, the loading factor, and the size of one jelly bean.
- Use the values to make an integer estimate of the number of jelly beans that can be placed in the indicated jar.
- To make your estimate as accurate as possible, all computations should be decimal.
- To make your estimate as accurate as possible, use Python's estimate of π when needed.
- In meeting the problem requirement of producing an integer estimate, do not round your decimal estimate. The extra bean produced by rounding would not fit in the jar.
Two different sample runs
Enter jelly bean length (cm): 1.52
Enter jelly bean height (cm): 0.9
Enter jar size (mL): 500
Estimate of jelly beans in the jar: 433
Enter jelly bean length (cm): 2.0
Enter jelly bean height (cm): 1.0
Enter jar size (mL): 25
Estimate of jelly beans in the jar: 13