How to Count Jelly Beans in a Jar

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You’re trying to guess closest to the number of jelly beans in a jar. You aren’t allowed to take them out and count them, so you need to be tricky. The best you can do is to estimate. You can do this by assuming that the jelly beans are fairly evenly distributed within the jar, and employing some basic geometry. First the height and circumference of the jar must be determined, using jelly beans as the unit of measurement. The volume of the jelly beans can then be calculated using a mathematical formula.

Bean Counting

Beans in a Box

You can use the same technique to calculate the number of jellybeans in a see-through rectangular or square box. To calculate the volume of the box, use this formula: Volume = length of box x width of box. If the jellybeans happen to be in a spherical container, calculate the volume of the container using this formula:

\text{volume}=\frac{4}{3}\pi 4^3

where r is the radius of the sphere.

    Measure the jars height in jelly beans.
    ••• Adam Korst/Demand Media

    Count the number of jelly beans that intersect with a line stretching from the top of the jar to the bottom. To make the line, you can stretch a piece of string, lay down a piece of tape or hold up a strip of paper. Count every jelly bean that the line crosses. This is the height of the jar in jelly beans.

    Count the number of jelly beans that intersect with a line that goes around the jar. Use the same method as above. If you can’t reach all the way around the jar, go half way around and multiply by 2. This is the circumference of the jar in jelly beans.

    One jelly bean is a unit of distance in this exercise.
    ••• Adam Korst/Demand Media

    Calculate the volume of the jar in jelly beans using the following formula:

    \text{volume}=\frac{(\text{circumference})^2\times \text{ height}}{4\pi}
    Count only whole jelly beans.
    ••• Adam Korst/Demand Media

    Round to the nearest jelly bean unless you think there might be broken pieces in the jar.

    Things You'll Need

    • Strips of paper
    • Tape
    • String
    • Calculator

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