March Madness
Geometry
Name: ____________________________________
Date: __________________
Pd.: _______
Geometry
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.
2.
B.
C.
D.
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
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
8.
Neglecting the thickness of the basketball, what is the volume of the basketball? Again, include correct
units.
volume = _______________________
9.
10.
Suppose that a basketball (a very elastic one) was overinflated so that the volume was 2,000 in3.
a.
What would be the diameter of the new basketball? diameter = _______________________
b.
Will this basketball be able to fit through the rim?
_______________________
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
March Madness
Geometry
Answer Key
Geometry
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.
2.
B.
C.
D.
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
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 = __254.47 in2_________________
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 = ___71.63 in2____________________
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 = ___286.52 in2____________________
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 = ____2292.16 lbs___________________
March Madness Geometry--An Activity by [Math]2
Page 5
8.
Neglecting the thickness of the basketball, what is the volume of the basketball? Again, include correct
units.
volume = _____456.05 in3__________________
9.
10.
Suppose that a basketball (a very elastic one) was overinflated so that the volume was 2,000 in3.
a.
What would be the diameter of the new basketball? diameter = ___15.63 in_______________
b.
Will this basketball be able to fit through the rim?
___Yes.____________________
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