Final answer:
The diameter of a ball that rolls without slipping and covers 3.5 meters after making 12.0 revolutions is calculated by dividing the total distance by the number of revolutions to find the circumference, and then dividing by π to find the diameter.
Step-by-step explanation:
The student has asked how to find the diameter of a ball that rolls without slipping and covers a distance of 3.5 meters after making 12.0 revolutions. To solve this, we need to recall that the circumference of a circle (or ball) is given by the formula ¡ = πd, where ¡ is the circumference and d is the diameter.
Since the question states the ball makes 12.0 revolutions, we multiply the number of revolutions by the circumference to find the total distance rolled. The equation can be rearranged to solve for the diameter:
d = ¡ / π
First we calculate the total circumference covered by multiplying the distance by the number of revolutions:
Total distance = Circumference per revolution x Number of revolutions
3.5 m = ¡ x 12.0
Then solve for the circumference per revolution:
¡ = 3.5 m / 12.0
Now that we have the circumference per revolution, we use the circumference formula to find the diameter:
d = ¡ / π = (3.5 m / 12.0) / π
After calculating this, we get the diameter of the ball.