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.
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.
