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Volume of a cylinder (a.k.a. Morton Salt Girl)
MATH 1050 - Mathematical Foundations 1
Volume of a cylinder (a.k.a. Morton Salt Girl)

Volume of a cylinder (a.k.a. Morton Salt Girl)

Author: Christopher Danielson

To apply volume of a cylinder to predict the outcome of a simple kitchen-based experiment.

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The volume of a cylinder is found in the same way as the volume of other prisms: Area of the base multiplied by the height of the prism. A cylinder has a circular base, so its area is:

B equals pi r squared

And then the volume of the prism is:

V equals B times h space or
V equals pi r squared h

Technical note: A cylinder is not technically a prism, as the mathematical definition of a prism includes the restriction that a prism has a polygon for a base. A circle is not a polygon, so a cylinder is not a prism. But conceptually, they're the same thing. And there really is no mathematical trouble caused by thinking of a cylinder as a circular prism.

Now on with the show...

The problem

New package of salt on the right. Empty Tupperware container on the left.

When we pour the salt into the Tupperware, will the container fill? Will it spill?

Make a gut instinct guess first.

Useful information for answering these questions follows...

Salt data 1: rulers

Do you like to compute precisely? Then use this data set.

If you prefer to compare (twice as tall, etc.), use the next data set.

Salt data 2: comparisons

Supplementary salt data

After you have made your prediction, the information here might be helpful in finalizing your guess.

Before you look at the slides, ask yourself this question: "How full do you think the blue package is before it is opened?"

And now the answer...

Will it fill? Will it spill?

Post your calculations

Use the Q&A to post your computations. How does your solution compare to the observed one?