Question

help i cant figure this out?
Two gears are connected and are rotating simultaneously. The smaller gear has a radius of 4 inches, and the larger gear has a radius of 7 inches.
Part 1: What is the angle measure, in degrees and rounded to the nearest tenth, through which the larger gear has rotated when the smaller gear has made one complete rotation?
Part 2: How many rotations will the smaller gear make during one complete rotation of the larger gear?

Answer 1

heres the picture of the gears

Answer 2

Calculate how far a point would travel around the perimeter (circumference) of the small gear for one revolution. In other words calculate the perimeter of the smaller gear.

Answer 3

The first step in finding the answer is to find the circumference of each gear. \[circumference = 2PIr\]

2(3)pi = 6pi
2(7)pi = 14pi

Answer 4

(I couldn't find the pi symbol...)

Answer 5

@radar Do you want to take this question?

Answer 6

Use 3.5 instead of 3. No you have the student on the right path.

Answer 7

Oh, I thought it was 3 not 4. Oops xD Sorry!! I read that wrong

Answer 8

@Jadeishere so 2(3.5)pi = 6pi like @radar said?

Answer 9

I may have goofed, use the diameter or two radius.

Answer 10

Well, let's change it to 4, cause I read it as 3. My mind does crazy things, I apologize.
Kay, backtracking.

\[2\pi(4) = 8\pi\]
\[2\pi(7) = 14\pi\]

Answer 11

So then, to get the angle measure in degrees, we have to divide the smaller gears circumference by the larger gears circumference then multiply it by 360 degrees.

\[\frac{ 8\pi }{ 14\pi } * 360\]

Answer 12

That can be further simplified to \[(\frac{ 8 }{ 14 })*360\]

Answer 13

You can actually just simplify that right back down to \[(\frac{ 4 }{ 7 }) * 360\]
That may seem like a bit of a circle, but make sure to take every necessary step.

Answer 14

The number you get for that, will be the answer, in degrees, to Part 1.

Answer 15

@Jadeishere ok so i got 205.7142857 when i solved the equation

Answer 16

Then, like it said, round to the nearest tenth. :)

Answer 17

@Jadeishere oh so 206?

Answer 18

@adeishere Love your profile.

Answer 19

Tenth, not whole number :)
A tenth is any decimal from
0.1 - 0.9

So it'd still be 205.7_____

Is 0.7 the nearest tenth, or can you round up from there?

Answer 20

Thanks @radar

Answer 21

@Jadeishere ??? um i guess you can ??????????

Answer 22

Rounding up or rounding down;

Up = 0.75+
down = 0.74-

So is the number directly to the right of 205.7 greater than 5 or less than 5?

Answer 23

@Jadeishere oh it was less than

Answer 24

So we round down to 205.7 :)

The answer to Part 1 is 205.7 degrees :D

Now for Part 2. This one is quite a bit simpler than than the previous Part.

This time, all you have to do is divide the larger radius by the smaller radius :)

Answer 25

@Jadeishere ah ok!! gimmie a bit d:

Answer 26

@Jadeishere 1.75?

Answer 27

Yes! Great job! :D

Answer 28

Great work @supersquidsisters
I'm glad I was able to help you! :)

Answer 29

@Jadeishere thank you soo much!!! you were such great help!!

Answer 30

I'm glad to hear :)