## Assignment 9 — problem solving

### Program bean_count.py

• 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