Parts of Areas and Circumferences of Circles 04:21 minutes

Video Transcript

Transcript Parts of Areas and Circumferences of Circles

The world’s greatest polar animals from the north and south poles are gathering once again in Antarctica for the 5th Annual Polar Games. During the opening ceremony, some of the event coordinators are still trying to find a suitable location for a few events. Luckily, they find two ice floes that may work. Both of them are in the shape of parts of circles, also known as sectors. To help the organizers decide which ice floe to use, they'll have to know about the parts of areas and circumferences of circles. There are three events: Penguin Sumo Wrestling, Polar Bear Figure Skating, and Walrus Swimming. The most important value for the Penguin Sumo Wrestling and Polar Bear Figure Skating events is the surface area of the ice floes. But in Walrus Swimming, since they race along the outside of the ice, they'll need to know how long the circumference of the ice floe is. Ice Floe 1 is ⅓ of a circle with a radius of 30 meters. Ice Floe 2 is ¾ of a circle with a radius of 10 meters. Let’s first calculate the area of Ice Floe 1. The formula to find the area of a circle is pi 'r' squared. When calculating the area of a sector, we multiply the area of the circle by the fraction of the circle we want to calculate. Since Ice Floe 1 is a third of a circle, the area of this ice floe is one third times pi times the radius squared. We can substitute in 30 meters for the radius and, using 3.14 for the approximation of pi, gives us a value of about 942 square meters. Now let’s calculate the area of Ice Floe 2. This time, we use three fourths for the fractional value and 10 meters for the radius. And using 3.14 for the approximation of pi, gives us a value of about 235.5 square meters. We can see that the organizers should use Ice Floe 1 for Polar Bear Figure Skating, since they need more area for all the jumps and turns and Ice Floe 2'll be used for Penguin Sumo Wrestling. Now, we just need to figure out which ice floe to use for Walrus Swimming. Remember, the circumference of the ice floe is the most important factor for this event. So let’s measure the two circumferences. First, we look at Ice Floe 1. The formula to find the circumference of a circle is 2 pi 'r'. Because the diameter is exactly two times the radius, you may see circumfence also written as pi 'd'. Just like with area, the circumference of part of a circle is the fractional part of the circle multiplied by the circumference of the entire circle. So, to find the circumference of Ice Floe 1, we need to multiply one third times two times pi times the radius. Substituting 3.14 for pi, and 30 meters for the radius just like we did before, we get approximately 62.8 meters. And finally, for the circumference of Ice Floe 2. Remember, that the fractional part is 3/4 and the radius is 10. Just as before, we use 3.14 to approximate pi which gives us approximately 47.1 meters. Floe 1 is the better choice, especially if the race is 1000 meters long. We don't want the walruses getting dizzy! To review: the area of a circle is pi 'r' squared and the circumference of a circle is 2 pi 'r'. And the area and circumference of a part of a circle is the fractional part of the circle multiplied by the original formulas. Let's get back to the games already in progress. Just look how gracefully this polar bear skates! Look at that pirouette! ...uh oh...the polar bear is now an ice bear!