Calculation of Circumference

To determine the distance covered by the scooter's wheel in one revolution, we need to calculate its circumference. The formula for circumference is:

C = πd

where C is the circumference, d is the diameter, and π is a constant value of approximately 3.14.

Substituting the given diameter of 70 cm into the formula:

C = π × 70 cm
C = 219.8 cm

Calculation of Distance Covered

Now that we know the circumference of the wheel, we can calculate the distance covered by the scooter in one revolution. Since the circumference is the distance traveled in one revolution, the distance covered by the scooter in n revolutions would be:

distance = n × circumference

Substituting the values given in the question:

distance = n × 219.8 cm
distance = n × 2.198 m

We want to maintain a speed of 33 km/hour, which is equivalent to:

33,000 m/hour
= 550 m/minute (since 1 hour = 60 minutes)
= 9.17 m/second (since 1 minute = 60 seconds)

We can now set up an equation to solve for n:

9.17 m/second = distance/time
9.17 m/second = n × 2.198 m / time
time = n × 2.198 / 9.17 seconds

Since we want to find the number of revolutions required to maintain this speed for 1 second, we can substitute time = 1 second and solve for n:

1 second = n × 2.198 / 9.17
n = 0.232 revolutions

Rounding this value to the nearest whole number, we get:

n = 0.232 ≈ 0.25

Therefore, the number of revolutions the scooter's wheel must make to maintain a speed of 33 km/hour is 0.25 or 1/4 of a revolution, which is equivalent to 250 revolutions. The correct answer is option C.