Round all answers to the nearest hundredth of an inch. A. B. C. D.
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1 Geometry March Madness Geometry Name: Date: Pd.: Directions: Now is the season of March Madness, the single-elimination NCAA Division I Basketball Tournament that currently consists of 68 teams vying for the national championship. In this activity, you will use math to explore the geometry of what it really means to put that ball through the net by looking at diameter, radius, volume, and area. Round all answers to the nearest hundredth of an inch. 1. In the photos shown below, notice that the relative size of the basketball to the rim is different for each photo. Which of the images below best shows the correct relationship between the diameter of a hoop and a standard-sized basketball? A. B. C. D. 2. The circumference of a men s NCAA basketball is 30 inches. What is the diameter of the basketball? diameter = 3. The inside diameter of a basketball rim is 18 inches. If a basketball were centered within a rim, what is the distance between the edge of the basketball and the rim? distance between the basketball and the rim = March Madness Geometry--An Activity by [Math] 2 Page 1
2 4. What percent of the rim s diameter is taken up by the ball? Which of the images from Question 1 looks like the best estimate? 5. a. Calculate the area of the opening inside a basketball rim. A = b. Consider a circle that would pass through the center of the basketball sphere (a great circle ). What would be the area of this circle? A = c. The circle s area in part (b) would make up what percentage of the area found in part (a)? 6. Calculate the total surface area of the basketball. Include correct units. surface area = 7. The men s NCAA basketball has a pressure of 8 pounds per square inch. What is the total force exerted by the air on the inside of the ball? Include correct units. total force = March Madness Geometry--An Activity by [Math] 2 Page 2
3 8. Neglecting the thickness of the basketball, what is the volume of the basketball? Again, include correct units. volume = 9. Suppose that a basketball (a very elastic one) was overinflated so that the volume was 2,000 in 3. a. What would be the diameter of the new basketball? diameter = b. Will this basketball be able to fit through the rim? 10. Besides clearance to the rim, what aspects of a basketball game might be affected by an over-inflated basketball? March Madness Geometry--An Activity by [Math] 2 Page 3
4 Geometry March Madness Geometry Answer Key Directions: Now is the season of March Madness, the single-elimination NCAA Division I Basketball Tournament that currently consists of 68 teams vying for the national championship. In this activity, you will use math to explore the geometry of what it really means to put that ball through the net by looking at diameter, radius, volume, and area. Round all answers to the nearest hundredth of an inch. 1. In the photos shown below, notice that the relative size of the basketball to the rim is different for each photo. Which of the images below best shows the correct relationship between the diameter of a hoop and a standard-sized basketball? A. B. C. D. 2. The circumference of a men s NCAA basketball is 30 inches. What is the diameter of the basketball? diameter = 9.55 in 3. The inside diameter of a basketball rim is 18 inches. If a basketball were centered within a rim, what is the distance between the edge of the basketball and the rim? distance between the basketball and the rim = 4.23 in March Madness Geometry--An Activity by [Math] 2 Page 4
5 4. What percent of the rim s diameter is taken up by the ball? 53.06% Which of the images from Question 1 looks like the best estimate? D 5. a. Calculate the area of the opening inside a basketball rim. A = in 2 b. Consider a circle that would pass through the center of the basketball sphere (a great circle ). What would be the area of this circle? A = in 2 c. The circle s area in part (b) would make up what percentage of the area found in part (a)? 28.15% 6. Calculate the total surface area of the basketball. Include correct units. surface area = in 2 7. The men s NCAA basketball has a pressure of 8 pounds per square inch. What is the total force exerted by the air on the inside of the ball? Include correct units. total force = lbs March Madness Geometry--An Activity by [Math] 2 Page 5
6 8. Neglecting the thickness of the basketball, what is the volume of the basketball? Again, include correct units. volume = in 3 9. Suppose that a basketball (a very elastic one) was overinflated so that the volume was 2,000 in 3. a. What would be the diameter of the new basketball? diameter = in b. Will this basketball be able to fit through the rim? Yes. 10. Besides clearance to the rim, what aspects of a basketball game might be affected by an over-inflated basketball? Sample answers may include: 1. changing the players grip on the ball 2. Changing the amount of bounce the ball will have (coefficient of restitution) March Madness Geometry--An Activity by [Math] 2 Page 6
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