Question 2:

A basketball has a diameter of 23 cm. How many times will the basketball roll from one end of the court to the other if the court is 29 meters long? (Round to the nearest whole number.)



Answer :

To determine how many times a basketball with a 23 cm diameter needs to roll to cover a distance of 29 meters, we can follow these steps:

1. Convert the diameter from centimeters to meters:
Since 1 meter is equal to 100 centimeters, we divide the diameter by 100 to convert it to meters.
[tex]\[ \text{Diameter in meters} = \frac{23 \text{ cm}}{100} = 0.23 \text{ meters} \][/tex]

2. Calculate the circumference of the basketball:
The circumference of a circle (or basketball in this case) can be calculated using the formula [tex]\(C = \pi \times d\)[/tex], where [tex]\(d\)[/tex] is the diameter.
[tex]\[ \text{Circumference} = \pi \times 0.23 \text{ meters} \][/tex]
Substituting the value of [tex]\(\pi \approx 3.14159\)[/tex], we get:
[tex]\[ \text{Circumference} \approx 3.14159 \times 0.23 = 0.722566 \text{ meters} \][/tex]

3. Calculate the number of rolls needed to cover the distance:
To find how many times the basketball needs to roll to cover 29 meters, we divide the total distance by the circumference of the basketball.
[tex]\[ \text{Number of rolls} = \frac{29 \text{ meters}}{0.722566 \text{ meters}} \approx 40.1347 \][/tex]

4. Round the result to the nearest whole number:
Rounding 40.1347 to the nearest whole number, we get:
[tex]\[ \text{Number of rolls (rounded)} = 40 \][/tex]

So, the basketball would need to roll approximately [tex]\( \boxed{40} \)[/tex] times to cover a distance of 29 meters.