Bambi is restoring a clock with a broken gear. A fragment of the small gear has 5 teeth . a larger unbroken gear has 18 teeth and is 2cm in dia.She knows that for every 2 times the large gear turns the smaller gear turns 3 times. How much cm of the perimeter on the broken gear is missing teeth.

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?

thanks

To find out how much of the perimeter on the broken gear is missing teeth, we need to determine the ratio of the number of teeth on the smaller gear to the number of teeth on the larger gear.

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.