Have your parents ever asked you how much candy you’ve eaten after seeing you empty a bag? Today you will learn how to calculate that amount into cubic centimeters, which should be enough to confuse them and get them off of your back.
- Bag of M&Ms
- Measuring cup in milliliters (mL)
- Clay or bread
- Ruler with centimeters (CM)
- Paper, pencil, and calculator
We are going to take three measurements to find the Volume.
- Count out 100 M&Ms.
- Fill your measuring cup to 100mL with water.
- Poor your M&Ms into the water and write down the measurement. (This will likely not be exact, the water level may be somewhere between 100-200mL or 150-200mL depending on the markings on your measuring cup. Do your best to estimate the number)
- Next subtract 100mL from this number. This is the volume for 100 M&Ms.
- Divide 100 the volume of 100 M&Ms. This will give you the volume for 1 M&M.
For example, the water level of the measuring cup for my experiment fell between 150-200 mL, closer to 150. I wrote down 160 mL. 160 mL – 100 mL = 60 mL. 60 mL / 100 = .6 mL. So the volume of 1 M&M is .6 mL.
Now we will convert this into cubic centimeters (cm3). Which is easy because 1 mL = 1 cm3. So .6 mL = .6 cm3. You can write this number down as your Actual Volume.
- Count out 10 M&Ms.
- Spread your clay evenly across a piece of paper. Or take out a piece of bread.
- Place your M&Ms into a row across your clay or bread, be sure to not leave any spaces, and have them evenly lined up. Measure the length of the M&Ms in centimeters (cm).
- Write this number down, then divide by 10. This will give you the diameter of 1 M&M. Write down the diameter. Then divide the diameter by 2 to get the radius and write this number down.
For example, the length of my 10 M&Ms was 130 cm. 130 cm / 10 = 1.3 cm. My diameter is 1.3 cm. 1.3 cm / 2 = .65. My Radius is .65 cm.
Now we will use these measurements to find the volume in 2 ways, sphere and cylinder. To do this you are going to go to this website, because this is easier than trying to figure this out. You are going to find 2 calculators on this page, Sphere Volume and Cylinder Volume. Make sure you use the drop down arrow for both of these and change the measurement to centimeters (it is by default feet). Enter the information into the calculator and it will give you the volume in cubic centimeters (cm3).
My calculations came out to:
Cylinder – 1.73 cm3
Sphere – 1.15 cm3
I now have 3 different measurements for the Actual Volume of an M&M! Are any of these correct? We will do 1 more calculation to see if we get any similar results.
Take those 10 M&Ms from the previous measurement out of the clay. Smooth down your clay so it is nice and even again. Place your M&Ms on their side (so they are standing up) into the clay. Make sure they are evenly lined up with no space between them. Then take the measurement with your ruler. Write down this number and then divide it by 10, this will give you the width of 1 M&M. Divide this number by 2 to give you the radius of the short side of the M&M.
For example, my length for 10 M&Ms was 6.6 cm. 6.6 cm / 10 = .66 cm. My diameter of 1 M&M is .66 cm / 2 = .33 cm. My radius is .33 cm. Write these numbers down for your short side.
Now we are going to use these numbers to make 2 more calculations, the Sphere Volume and Ellipsoid Volume.
Go back to the calculator page and plug your information into these calculations. Remember to change feet to centimeters. The Ellipsoid Volume will need a measurement from your second measurement (the radius from the long side).
Sphere – .15 cm3
Ellipsoid – .58 cm3
Now I have 2 more measurements for the Actual Volume in cm3. But If I look at all of my numbers I see that 2 of the measurements are very, very close. My first measurement using water, and my last measurement for the Ellipsoid are only .02 cm3 apart. Based on this I am going to say that the Actual Volume of 1 M&M is .59 cm3. Why? Figure that out for yourself. Ask yourself why these two measurements came out so close and why, based on the shape of an M&M, would these give me the closest measurement.
Using this system, find the Actual Volume of your favorite candy. And the next time your parents asked you how much candy you have eaten you can tell them exactly how much in cubic centimeters, which should confuse them enough to leave you alone and let you eat your candy in peace.
I wish I was smart enough to come up with this experiment myself, but I am not. If you are interested in learning more about this experiment or would like to see more like it, visit this website.
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