All About Pi 05:17 minutes

Video Transcript

Transcript All About Pi

It's Thanksgiving at the Griswald house and the food is ready but granny Griswald notices that someone has eaten all the pumpkin pies! Granny Griswald has an idea! Call the best pumpkin pie delivery service in town, All About Pi(e)! The Griswald family just loves pumpkin pie. So, to satiate the family's dessert hunger, Granny must make sure that everyone has enough pie. Unfortunately, All About Pi(e) has changed their menu recently, and now only the radius of each pie is labeled. Let’s look at the largest pie. First, we notice that this pie is labeled r = 7. r' is a common variable used to stand for the radius of a circle. The radius is the distance from a circle’s center to its edge. The longest distance between one side of a circle to the other is called the diameter. The diameter is exactly two times the length of a circle’s radius in this case, the diameter is 14 inches. The diameter and radius are used to calculate the circumference and area of circles with one special ingredient...π!!! Pi is what mathematicians call an irrational number. This means that the number cannot be expressed in fraction form. It also means that we can use a shorter form of pi in our calculations. Two common approximations of pi are the decimal version, 3.14, which is accurate to two places and the fraction form, 22 over 7, which is accurate to three places. But for us, using 3.14 for our calculations will be good enough. Π is the ratio between a circle’s radius or diameter and its area and circumference, respectively. For example, if you want to know the area of a circle, you simply have to use the formula: pi 'r' squared. Let’s use this formula to calculate the visible area of the largest pie. First, we take our formula, ‘A’ equals pi ‘r’ squared and we substitute 7 for ‘r’. 7 squared, as you may already know, is 49. We can write our answer in two ways: 49 pi, or in decimal form -- using 3.14 for pi -- about 153.94. Granny thinks 10 of these pies will satisfy the Griswald family and it wouldn't be the worst thing if there are leftovers! Since it's a special occasion Granny decides to get a special topping on the crust of the pie whipped cream and walnuts. Let’s take a look at the distance around each pie, or its circumference. The formula for the circumference of a circle is circumference equals 2 'pi' 'r'. But, since the diameter is two times a circle’s radius, another way to represent this formula is to write it like this: 'c' equals pi 'd'. Just like with area, there are two ways to represent the circumference: 14π or in approximate decimal form...43.98. Confident that this is the size of pie she needs, granny orders 10 pies with the whipped cream and walnut crust, of course!!! The pies are ready and the owner of All About Pi(e) jumps in his pie-mobile and heads off to the Griswald’s. If the distance to the Griswald’s house is 50 feet, and the radius of the pie-mobile’s wheels are 15.915 inches how many revolutions do the wheels make between All About Pi(e) and the Griswald’s house? If we take the distance between these two points as 50 ft, or 600 inches and we know the circumference of a circle is given by the formula 2 pi 'r' we can find out how many rotations each wheel will make on the way to granny's house. Evaluating what we have, and using 3.14 for pi we can see that each wheel will make about 6 rotations between the two locations. Something smells good...and there's the doorbell! The pumpkin pies must be here!

Huh? How in the world did Russ Griswald get in there so fast?