If your kids are anything like mine, they love making amazing snowmen on wintery days — especially if they have off from school! Since NJ is presently in the middle of blizzard, and it happens to be Pi Day, I thought I’d put forth an epic idea: The Pi Day Snowman!
Here’s what you’ll need:
- Snow, lots and lots of snow
- Creative kids willingto brave the cold
- A dressmaker’s tapemeasure (the flexible kind) or a roll of string and a meterstick, tapemeasure, etc.
- Pencil and paper (or another way to record your measurements)
- A calculator (optional)
The first step is pretty simple: Build a snowman. Go for the classic type — three spheres of snow stacked up high, with the largest on the bottom and the smallest on top, as the head. Decorate him. Give him a scarf. You know the drill.
Now, it’s time for the math! Using your flexible tapemeasure measure the circumference of the largest ball of snow, wrapping the tapemeasure around the the widest part of the ball. If you don’t have the flexible tapemeasure, no problem. Wrap a length of string around the widest part fo the ball, mark the width and then compare it against a meterstick or traditional tapemeasure to get the length.
Now measure the diameter of the largest sphere. This is a bit tough to do accurately without damaging the snow man. (No snowmen we harmed in the making of this blogpost.) So there are two ways to go about it: 1) The less accurate method, of holding your tapemeasure straight across the widest part and eyballing it or 2) The more accurate, but more challenging method of slowly “sawing” the tape measure into the packed snow of the sphere acorss the widest part until it is centered and measuring and distance. I’ll leave it to you, to decide which methods you prefer.
Great. Now it may be time to take out that calculator. As you may recall from school, the circumference of a circle is calulated using the formula C=2πr, which is 2 x π x radius. The radius is half the diameter of a circle, so 2r=diameter (d), of r=d/2. Pi (π) is commonly know as 22/7 or 3.14. Here’s the thing. That number comes from somewhere. It’s not magic; it’s math! It was first calculated by the Ancient Greeks (Thanks Archimedes!) as a relationship between the circumference and diameter of a circle.
Well, what do you know? We have the circumference and diameter of our snowman spheres! We can calculate pi for ourselves. Let’s see if is works. Just divde the circumference of your ball by the diameter you recorded. You should get a number close to 3.14, depending on how accurate your measurements were. Doesn’t matter how big the ball is, that relationahip will always be the same. Always. That’s what pi is all about! Pretty cool, right?
Of course, from there you can go ahead and calculate the volume of your sphere V=4/3πr3. Or the surface area using the formula A=4πr2.
So enjoy the snow and enjoy the math! Happy Pi Day!