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Abstract
Have your parents ever found you munching on candy and asked you, "How much candy did you eat?" Instead of saying, "I do not know?" and getting in trouble, maybe you would rather say, "I ate precisely 10.7 cubic centimeters of candy, Mom." Make your parents proud of their candy-eating genius child (you) with this simple science project.
Summary
Areas of Science
Pure Mathematics
Difficulty
Time Required
Very Short (≤ 1 day)
Prerequisites
None
Material Availability
Readily available
Cost
Very Low (under $20)
Safety
No issues
Credits
Sara Agee, Ph.D., Science Buddies
Teisha Rowland, Ph.D., Science Buddies
- M&M'S® is a registered trademark of Mars, Inc.
Objective
Investigate which formula is the most accurate for estimating the volume of an M&M'S® candy.
Introduction
Geometry is the study of how to use math to describe and investigate different points, lines, and shapes. The way that a shape is described in geometry is with a formula, which is simply a mathematical way to calculate different properties of a shape like size, area, or volume. Volume is a unique property of three-dimensional shapes because three-dimensional shapes take up space in three different directions. Most real-world objects are three dimensional: balls, cars, food, etc.
The problem with geometric formulas is that they describe "perfect" or "ideal" shapes. A sphere is an "ideal" three-dimensional shape that is perfectly circular in all directions. Even though a ball is spherical in shape, it is not a perfect sphere. If geometric formulas describe "ideal" shapes and not "real" shapes, then how are they useful in the "real" world?
Most real-world shapes are not simple shapes and use complex geometry to be calculated. The properties of real-world shapes can also be approximated, or estimated, to the best possible measure with a geometric formula. This is called making a geometric model, and the most important part of making a good geometric model is choosing the formula that best describes the object. Even the most irregular objects can be modeled by using geometry: cars, airplanes, electronics, plastics, food, etc. Geometric modeling is very important for manufacturing because a product needs to have the same shape, made the same way, every time.
In this mathematics science project you will use geometry to produce a mathematical model of an M&M'S candy. If you look closely, you will see that the volume of an M&M'S candy is a bit irregular - it is not quite perfectly round. It looks like a ball shape (sphere) that has been squished on one side, as shown in Figure 1 below. You will test three different formulas (one for a sphere, one for a cylinder, and one for an ellipsoid) to see which formula makes the best geometric model of an M&M'S candy. You will test each formula by using it to calculate the volume of an M&M'S candy and then you will compare your result to the actual volume of a single piece of candy.
Figure 1. An M&M'S candy looks like a sphere that has been flattened on one side. The blue M&M'S; on the left is shown from the top, while the orange M&M'S; on the right is shown from the side.
Terms and Concepts
- Geometry
- Formula
- Volume
- Model
- Radius
- Diameter
- Height
- Sphere
- Cylinder
- Ellipsoid
Questions
- What is a geometric model? Why can it be useful?
- Which formula do you think will calculate the most accurate volume of an M&M'S® candy? Why?
- How are geometric formulas different from each other?
- What other ways can you use geometric formulas to measure real-world objects?
Bibliography
You can do further research by visiting the following websites, which give information about geometry and calculating areas and volumes:
- # Link Name="Math_p022.1" Value="HtmlAnchor" HtmlText="MathIsFun.com" #]. (n.d.). Geometry.. Retrieved December 3, 2012.
- # Link Name="Math_p022.2" Value="HtmlAnchor" HtmlText="Math2.org" #]. (n.d.). Math2.org Math Tables: Areas, Volumes, Surface Areas.. Retrieved December 3, 2012.
For help creating graphs, try this website:
- National Center for Education Statistics, (n.d.). Create a Graph. Retrieved June 25, 2020.
Materials and Equipment
- M&M'S® (110). One 7-oz (198-g) bag holds about 210 M&M'S.
- Metric ruler that measures in centimeters (cm)
- Metric measuring glass or cup that measures in milliliters (mL). Must measure at least 200 mL.
- Water
- Table or countertop
- Piece of paper
- Clay or Play-Doh. Use a small amount that you do not mind ruining.
- Computer with Internet connection
- Lab notebook
Experimental Procedure
- First measure the actual volume of an M&M'S candy with a water displacement test.
- In your lab notebook, make a data table like Table 1. You will be recording your measurements in it.
- Fill the metric measuring glass or cup with 100 milliliters (mL) of water.
- Make sure it has exactly 100 mL. You can do this by looking at where the top of the water is when your eyes are level with it.
- Add 100 M&M'S to the water.
- Why do you think you are using 100 M&M'S instead of just one? Dropping just one M&M'S into a glass of water will not change the water level by much. By using 100 M&M'S you will be able to more easily see a larger change in the water level that will be easier to measure. You can then divide the change you see for a hundred M&M'S by the number 100 to calculate the volume of a single M&M'S candy.
- In the data table in your lab notebook, record the new, final volume of water.
- Estimate the new volume as closely as you can based on the marks on the glass. For example, if it is right between a mark that says "150" and one that says "175," then you can estimate that it is at about 163 mL.
- Subtract the beginning volume of water (100 mL) from the new volume of water (that you just measured) to calculate the actual volume of the 100 M&M'S. Write this in your data table.
- To continue the example above, if the volume for 100 M&M'S is 163 mL, then you do this calculation: 163 mL - 100 mL = 63 mL. Meaning that 100 M&M'S have a volume of 63 mL.
- Divide your answer by 100. This is the actual volume of a single M&M'S candy in milliliters. Write this answer in your data table. You will be referring to this value later.
- In our example you would do this calculation: 63 mL / 100 = 0.63 mL. Meaning that each M&M'S candy has a volume of 0.63 mL. Remember, this is just an example of the calculations. You will have to do the experiment yourself to see what the real volume is!
Actual Volume (mL) | |
Starting Volume (mL) | 100 mL |
Final Volume (mL) | |
Actual Volume of 100 M&M'S (mL) | |
Actual Volume of 1 M&M'S candy (mL) |
Table 1. In your lab notebook, make a data table like this one. You will be recording your water displacement measurements in it, which you will be using to figure out the actual volume of 1 M&M'S candy.
- Next you will test different mathematical formulas to see which one is the best geometric model of an M&M'S® candy. Before doing this, make sure you do your background research and know what the terms radius, diameter, height, sphere, cylinder, and ellipsoid mean.
- You will be making some careful measurements with (fresh!) M&M'S candies to use in the different formulas. In your lab notebook, make a data table like Table 2 to record your measurements in.
Long Side (cm) | Short Side (cm) | |
Diameter of 10 M&M'S | ||
Diameter of 1 M&M'S candy (divide by 10) | ||
Radius of 1 M&M'S candy (divide by 2) |
Table 2. In your lab notebook, make a data table like this one. You will be recording your measurements in it, which you will be using to do calculations with different formulas.
- Measure the long side of 10 fresh M&M'S lined up in a row. (Do not use any of the M&M'S that you used in the water displacement test!) Do this by using the following neat little trick:
- Place a piece of paper on a clean table or countertop.
- On top of the paper, place a small amount of clay or Play-Doh.
- Flatten it and stretch it out into a little line. Make it run along the length of the ruler.
- Line up 10 fresh M&M'S on their flat side, end-to-end, as shown in Figure 2. Poke them into some clay to keep them in a neat row with each M&M'S touching the next and no gaps in between them.
Figure 2. To measure the long sides of 10 M&M'S, line them up length-wise in clay or Play-Doh, next to the ruler. This image only shows 4 M&M'S lined up, but you will be using 10 M&M'S.
- Measure the whole line of 10 M&M'S from end-to-end. Write this measurement in the new data table in your lab notebook. Write it in the "Long Side" column as the "Diameter of 10 M&M'S."
- Divide your answer by 10. This is the long diameter of a single M&M'S candy. Write the data in your data table.
- Divide your answer by 2. This is the long radius of a single M&M'S candy. Write the data in your data table.
- Remove the M&M'S from the clay.
- On the clay, line up the 10 M&M'S on their side so that you are measuring across the short side, or short diameter, as shown in Figure 3.
- Again, use the clay to hold the M&M'S in place in a neat row with each M&M'S® touching the next.
Figure 3. To measure the short sides of 10 M&M'S, line them up on their side in clay or Play-Doh, next to the ruler. This image only shows 4 M&M'S lined up, but you will be using 10 M&M'S.
- Repeat steps 5-8, but this time measure and do calculations for the short side of the M&M'S.
- In the data table in your lab notebook, record your measurements in the "Short Side" column.
- Next you will be making some calculations of volume using different formulas to see which one best calculates the volume of the M&M'S. In your lab notebook, make a data table like Table 3 to record your results for each formula.
- For the "Actual Volume" use the value you determined in step 1f. Note: One milliliter is the same as one cubic centimeter (cm^{3}). So, even though you determined the actual volume of one M&M'S candy in milliliters, you can write this value in cubic centimeters instead.
Calculated Volume (cm^{3}) | |
Actual Volume | |
Sphere - Long Radius | |
Sphere - Short Radius | |
Cylinder | |
Ellipsoid |
Table 3. In your lab notebook, make a data table like this one to record your results for each formula.
- If you are comfortable doing the math yourself, you can calculate the volumes of different shapes by hand using the formulas on this page. Otherwise you can search for an online volume-calculating tool like http://www.calculator.net/volume-calculator.html, where you can enter the relevant dimensions for each shape and it will calculate the volume for you.
- First you will calculate the volume of a sphere. You will be making the sphere calculation in two ways, with the long radius and the short radius.
- Calculate the volume of a sphere using the long radius. Write the answer in your data table next to "Sphere - Long Radius."
- Note: Since your measurements are in centimeters, the answers will be in cubic centimeters.
- Calculate the volume of a sphere using the short radius. Write the answer in your data table next to "Sphere - Short Radius."
- Next you will calculate the volume of a cylinder, using the radius and height of the cylinder. Write the answer in your data table next to "Cylinder."
- Next you will calculate the volume of an ellipsoid. Ellipsoids have three axes. Use the M&M'S long diameter value for two of the axes, and the short diameter value for one of the axes. Write the answer in your data table next to "Ellipsoid."
- Now you are ready to make a bar graph of your data. You can make one by hand or you can try using the Create a Graph website for kids from the National Center for Education Statistics.
- Along the x-axis (the horizontal axis), make one bar for each type of volume calculation you did, such as a sphere using the long radius, sphere using the short radius, cylinder, and ellipsoid. Also include a bar for the actual volume that you determined in step 1f.
- On the y-axis (the vertical axis) put the volume measurements in cubic centimeters (cm^{3}).
- How do each of the different calculated volumes compare to the actual volume that you measured? Which ones were more and which ones were less? Why do you think this is? Which calculation came the closest? Which formula do you think is the best one to use for an M&M'S candy?
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Variations
- Another way to look at your data is to calculate the difference between each calculation and the actual volume measurement. You can do this by subtracting the actual volume from the calculated volume for each formula. A bigger number is more different from the actual volume than a smaller number. You can also calculate something called the percent difference by dividing your answer by the actual volume. If you make another graph comparing the percent difference of each method, what does it show?
- You can use this same experiment to find the best formula to calculate any other volume. Try using it for an egg, a football, an apple, a bar of soap, or any other irregular shaped object. Just make sure that you choose an object that can safely be submerged in water! Which formula is the best?
- For a more advanced science project, you can try to investigate how the shape of a candy affects how well many of those candies pack together. Use the water displacement test on a couple differently shaped candies to determine the actual volume of a single candy. Then fill a measuring glass with a certain amount of each type of candy, one type at a time (without water). See how high this filled the glass and divide this total volume by the number of candies to determine how much space one candy took, on average, when taking packing into account. How much space does each type of candy take up in the measuring glass (when packing is taken into account) compared to the actual volume of one candy? In other words, which types of candies pack together the best? How do you think their shape affects this?
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General citation information is provided here. Be sure to check the formatting, including capitalization, for the method you are using and update your citation, as needed.
MLA Style
Science Buddies Staff. "M&M Geometry." Science Buddies, 20 Nov. 2020, https://www.sciencebuddies.org/science-fair-projects/project-ideas/Math_p022/pure-mathematics/mms-geometry. Accessed 14 Mar. 2023.
APA Style
Science Buddies Staff. (2020, November 20). M&M Geometry. Retrieved from https://www.sciencebuddies.org/science-fair-projects/project-ideas/Math_p022/pure-mathematics/mms-geometry
Last edit date: 2020-11-20
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FAQs
How do you guess the number of M&Ms in a jar? ›
An approximate method to calculate the number of sweets in a jar, is to multiply the number along the width and length of the base by the number of sweets in the height of the jar. Granular Matter theory then tells us that on average a jar of mixed shapes will have about a 30% air gap in between the sweets.
What is the geometry of an M&M? ›An M&M indeed has an ellipsoid shape, specifically, a type called an oblate spheroid.
How many M&Ms fit in a cup? ›A: There are approximately 255 M&Ms in a cup (8 oz). A 38 oz bag is approximately 4.75 cups, so based on this math there are about 1,211 M&Ms in the bag.
How many M&Ms fit in a Mason jar? ›Based on the formula in the article, the amount of M&M's a mason jar can hold is as follows: A quart sized mason jar is 32oz in size and would be expected to hold about 1,019 M&Ms. A pint-sized mason jar is 16oz in size and would be expected to hold about 509 M&Ms.
How do you find the probability of M&Ms? ›The number of M&M's in a color is placed in the numerator, the total number of M&M's is placed in the denominator. (Example, If there are 6 red M&M's and 54 total M&M's, the probability of picking a red M&M is 6/54.)
What is the best way to guess the amount in jar? ›So, multiply the radius number by itself, and, to get a rough estimate, multiply this number by 3. EXAMPLE: With a radius of 5, your formula would be: Pi x 52 = 3 x 25 = 75 So, a single layer of items in the jar should be about 75 items.
What does the symbol m represent in geometry? ›The m in front of the angle notation refers to the measure of the angle labeled A, B and C (with vertex at B). By definition, the term congruent means "having equal length or measure". Segments are congruent. Angles are congruent.
What is the hypothesis for the M&M project? ›The null hypothesis in this investigation was that there should be no difference in expected percentage of colors of m&ms than there is in each individual packet of m&ms. m&m's Mars factory states that there is a specific percentage of each color within m&m Peanut and Plain packages.
How many mm is a 64 oz jar? ›Capacity | 1/2 gal., 64 oz. |
---|---|
Material | Glass |
Neck Finish | 83-405 |
Neck Width | 83 mm |
Dimensions | 4.89" Dia x 8.422" H |
Each Bulk M&M 2LB bags are retail-sealed from the manufacturer. There are approximately 500 pieces per pound.
How many cups is a 12 oz bag of M&Ms? ›
For the easiest conversion guide, twelve US fluid ounces (12 oz) make up 1.5 cups.
How many M&Ms are in a 10 oz bag? ›A perfect treat for candy dishes, baking, or for any fans of the beloved candy-coated chocolate candy! Each bag contains 10.0 oz. of chocolate candies. Bag contains: approximately 320 pieces (about 10 servings).
How many M&M's are in a 56 oz jar? ›With their soft, sweet chocolate inside a yummy candy shell? Melts you-know-where but not you-also-know-where? Don't you kind of want some, right now? Jar contains 62 ounces of Milk Chocolate M&M's Candy... that's about 1,750 pieces.
How many M&Ms are in a 3.14 oz bag? ›Therefore, 104 m&ms in the 3.14 oz bag.
How do you solve marginal probability? ›This can be calculated by one minus the probability of the event, or 1 – P(A). For example, the probability of not rolling a 5 would be 1 – P(5) or 1 – 0.166 or about 0.833 or about 83.333%.
What is the probability of M&M colors? ›30% brown, 20% yellow, 20% red, 10% orange, 10% green, and 10% blue.
How can I solve probability? ›Divide the number of events by the number of possible outcomes. After determining the probability event and its corresponding outcomes, divide the total number of ways the event can occur by the total number of possible outcomes. For instance, rolling a die once and landing on "3" is considered one event.
What can I fill a jar with for a guessing game? ›Simply fill a glass jar (or plastic) with popcorn, candy corn, or gummy worms and let your guests guess how much is in it. Taking the closest guess as the winner, he or she gets to keep the jar for a prize!
How many kisses fit in a 32 oz jar? ›Thanks for asking! 7 pieces per 31 grams is the serving size. You'll get approximately 400 pieces of Kisses.
How many M&M's are in a 42 oz jar? ›How many M&M's are in a 42 oz jar? Bag dimensions: 2.87 x 9.25 x 9.00 Inches. Weight: 42 ounces = 2 lbs 10 oz. Number candies/bag: approximately 1,344 pieces.
Is there an app to count candy in a jar? ›
Candy Counter is the #1 app for estimating the number of candies in a jar/glass/container. Select the type of candy and the type of container and Candy Counter will give you an estimate based on pre-determined candy volume and packing factor data.
What candy to use for guessing game? ›Candy Guessing Jars
You can use M&Ms, Reese's Pieces, Jelly Beans, or any type of candy you choose. Be sure, though, that you count exactly how many candies you place in the jar. The object of the game is to have guests guess the amount of candy; the closest guesser will win the whole jar!
Bag contains 16 ounces of Brach's Large Conversation Hearts Candy... that's about 140 pieces.
How many M&Ms are in a 1 oz bag? ›Each bag holds about 11 servings of your M&M'S candies, one serving is 1 oz (28g/about 32 pieces) of M&M'S. When should I place my order?
How many M&Ms are in a 62 oz box? ›Don't you kind of want some, right now? Jar contains 62 ounces of Milk Chocolate M&M's Candy... that's about 1,750 pieces. Made in the USA. Shipping Weight ~ 4 lbs.
What do you put in the punishment jar? ›What Is A Consequence Jar? Basically, it's a jar of consequences for your children in the event they break a household rule. No yelling, no idle threats. You simply have the child choose a slip of paper at random and whatever the paper says becomes their consequence.
What do you put in random jars? ›- Pop some coloured sand or beads and a tea light in your glass jar, to create a lantern. ...
- Use your glass jar to store delicious combinations of oils, spices, herbs and fruits for scenting your rooms. ...
- Create a cute terrarium.
- Make a 'happiness jar'.
Jar app is 100% safe and secure to use for your Daily Savings & Investments in Gold. It is powered by SafeGold and all payments happen over secure banking networks.
How many Hershey Kisses fit in a 32 oz jar? ›Thanks for asking! 7 pieces per 31 grams is the serving size. You'll get approximately 400 pieces of Kisses.
How do you check your kids candy? ›...
Give each piece a visual inspection for signs of:
- Discoloration to packaging.
- Holes or rips in the wrapper that have been resealed.
- Homemade treats that were provided from someone you don't know.