Closed-Ended Problem Algorithm:
Jelly Beans
Problem Statement: How many jelly beans will fit in a cylindrical jar 10 inches high and 8 inches in diameter?
ATTITUDE
This is a fun problem that may prove useful in the future for winning a guessing contest.
ACTIONS
Re-describe the problem:
What is the volume of the jar and what is the volume of a jelly bean and what is the packing factor (i.e., what is the volume fraction of the jelly beans in the filled jar
remembering there will be some empty space between the beans)?
Assumptions:
Assume the jelly beans are spheres.
Sketch the system:
SOLUTION PROCEDURE
Identify:
KnownsJar height (H= 10 inches) and jar diameter (D=8 inches).
Jelly bean diameter (d=0.5inches)
UnknownsSolid Fraction (the fraction of the jar volume occupied by beans, not including the void space between the beans).
Fundamentals:| Volume of the cylinder | = | π(D2/4)H in3 |
| = | 3.1416*((82)/4)*10 |
| = | 502.6 |
| Volume of one jelly bean | = | π(D3/6) in3 |
| = | 3.1416*(0.53/6) |
| = | 0.0654 |
| Look up the solid fraction of spheres packed together. It is ~0.65. |
| Volume of Beans | = | (Jar Volume)*(Solid Fraction) |
| = | 502.6*0.65 |
| = | 326.7 in3 |
| Number of Beans | = | (Volume of Beans)/(Volume of One Bean) |
| = | (326.7 in3)/(0.0654 in3 per bean) |
| = | 4,995 beans in the jar |
ACCURACY
Check and Recheck:
Explore the effects of cylindrical beans rather than spherical beans.Check the jelly bean dimensions.
If beans are cylindrical (D = 0.5in, H = 0.5in), redo the calculations.
| Volume of one jelly bean | = | π(D2/4)*H |
| = | 3.1416*(0.52/4)*0.5 |
| = | 0.0982 in3 |
Look up the solid fraction of cylinders packed together in jar. It is ~0.67. | | Volume of Beans | = | (Jar Volume)*(Solid Fraction) |
| = | 502.6*0.67 |
| = | 336.7 in3 |
| Number of Beans | = | (Volume of Beans)/(Volume of One Bean) |
| = | (336.7 in3)/(0.0982 in3 per bean) |
| = | 3429 beans in the jar |
The true number of jelly beans in the jar is probably between the two figures, since the beans are not truly spheres or cylinders, but this technique gives us a bracket that the true answer lies between.
Back to Chapter 2
FAQs
The act of summarizing is much like stating the plot of a play. For instance, if you were asked to summarize the story of Shakespeare's 'Hamlet,' you might say: It's the story of a young prince of Denmark who discovers that his uncle and his mother have killed his father, the former king.
What is the format of a summary note? ›
When writing a summary, remember that it should be in the form of a paragraph. A summary begins with an introductory sentence that states the text's title, author and main point of the text as you see it. A summary is written in your own words. A summary contains only the ideas of the original text.
What does a summary note do? ›
When you write a summary, you are demonstrating your understanding of the text and communicating it to your reader. To summarize is to condense a text to its main points and to do so in your own words. To include every detail is neither necessary nor desirable.
What is a short note of summary? ›
A summary is a short statement that summarizes or informs the audience of the main ideas of a longer piece of writing. Essentially, the summary is a short version of a longer text. The size of a summary can vary based on the type of writing, but most often they are no longer than a page.
Should I make summary notes? ›
Using notes and making summaries
Using your notes in an active way afterwards helps you to learn effectively. This might be through organising material into a meaningful structure, thinking about inter-relationships and relating what you are learning to examples or case studies or real-life situations.
What 3 things should a summary include? ›
Main points of the original text: This restates the main points the author conveyed. Supporting arguments: Here, you list the arguments that support the author's thesis or main idea. Final point: Conclude your summary with the final point from the author.
What is a short note on summarizing? ›
A summary is a short retelling of a longer written passage, containing the author's most important ideas. Summarizing helps improve both your reading and writing skills. To summarize, you must read a passage closely, finding the main ideas and supporting ideas.
How long should a summary be for notes? ›
A summary is not a rewrite—it's a short summation of the original piece. A summary paragraph is usually around five to eight sentences. Keep it short and to the point. Eliminate redundancies or repetitive text to keep your paragraph clear and concise.
How to create summary notes? ›
Summarise your notes on the topic from the various sources you have collected together. Draw together the main points from these notes, using headings and key points. Try to reduce these notes further to one side of A4 paper, using only the main headings and a few associated key words.
How to summarize when taking notes? ›
To summarize effectively, begin by reading your notes carefully and identifying the main theme, topic, or message of the material. Then, select the key points, facts, or arguments that support the main theme. Next, rewrite the key points in your own words using concise and clear language.
