Danny loves both basketball and math. While watching a basketball game, he gets an idea to create a math problem involving a basketball. The problem asks for the equation of a basketball using the information that a basketball has a circumference of 30 inches and diameter of 30 inches/π, with the center of the basketball at the origin (0,0) of the graph. The solution finds the radius of the basketball by taking the diameter (30 inches/π) and dividing by 2, getting approximately 4.7746 inches. Using the standard form of a circle equation and substituting the radius and center point values, the equation is determined to be (x – 0)2 + (y – 0)2 =

1. Problem 3: Basketball Game Created by Danny Ly

2. The Story Danny really loves basketball, but he also loves math too. So while he was sitting at a Phoenix Suns game watching his favorite player #17 shoot free throws he thought to himself…. “ What if I had made a math problem involving basketball? How about the basketball itself??? Yeah! I got a great idea!” So Danny grabbed some paper and started making a problem…..

3. Basketball Question The official circumference of a basketball is approximately 30 inches . The diameter would be 30inches/Π . Knowing these facts and having the centre of the basketball on the origin (0.0) , could you come up with an equation and a sketch of the basketball?

4. Solution: PART A The standard form of the equation of a circle is: (x - h )² + (y – k )² = r² the h stands for the x-coordinate of the centre of the circle the k stands for the y-coordinate of the centre of the circle ( h , k ) is the coordinates of the centre of the circle, circles do not have a vertex the r² stands for radius squared, if we have this value we can derive the radius from it using our understanding of the standard form of the equation of a circle we can find the equation of the circle in this problem and using the equation sketch the circle

5. Solution: PART B The question provides us with three key facts about the basketball that we can use: the circumference of the basketball is 30 inches the diameter of the basketball is 30 inches/ Π the centre of the basketball has to be on the origin (0,0) With these three facts we already know where the basketball is going to be on the graph when we sketch it, however in order to derive the equation from this and to sketch the basketball we need to know what the radius is. Remember that the diameter of a circle is directly two times longer then the radius of a circle: diameter = 2 X radius Therefore to find the radius we must take the diameter and divide it by two: radius = diameter / 2 radius = 30 inches/Π / 2 radius = approx. 4.7746

6. Solution: PART B continued… Having found the radius we can now derive the equation of the basketball: (x – h )² + (y – k )² = r² h = 0 k = 0 r = approx. 4.7746 r² = approx. 22.7973 Substitute in the values and we get: (x – 0)² + (y – 0)² = 22.7973  that is the equation of the basketball in standard form We can now make a sketch of the basketball on a graph:

7. THE END