clearly the smaller wheel has 2/3 the diameter of the larger wheel.
So, it has 2/3 * 18 = 12 teeth.
So, what is 7/12 of its circumference?
So, it has 2/3 * 18 = 12 teeth.
So, what is 7/12 of its circumference?
We are given that the smaller gear has 5 teeth and the larger gear has 18 teeth. We also know that for every 2 turns of the larger gear, the smaller gear turns 3 times.
To find the ratio of the number of teeth on the gears, we divide the number of teeth on the smaller gear by the number of teeth on the larger gear:
5 teeth / 18 teeth = 5/18
This means that for every 5/18 turns of the larger gear, the smaller gear turns once.
Now, we need to calculate the circumference of the larger gear.
The formula for the circumference (C) of a circle is given by the equation:
C = 2 * π * r
where π (pi) is approximately equal to 3.14159 and r is the radius of the circle.
Since we are given the diameter of the larger gear (2cm), we can calculate the radius (r) by dividing the diameter by 2:
r = 2cm / 2 = 1cm
Now we can calculate the circumference of the larger gear using the radius:
C = 2 * 3.14159 * 1cm = 6.28318cm
Next, we need to calculate the distance the larger gear travels in order for the smaller gear to turn once.
Since we know that for every 5/18 turns of the larger gear, the smaller gear turns once, we can calculate the distance traveled by the larger gear by multiplying the circumference by the ratio:
Distance = C * (5/18)
= 6.28318cm * (5/18)
≈ 1.736cm
Therefore, approximately 1.736cm of the perimeter on the broken gear is missing teeth.