I give medallssss!!

Two gears are connected and are rotating simultaneously. The smaller gear has a radius of 2 inches, and the larger gear has a radius of 8 inches.

two circles touching at one point. Larger circle has radius of 8 inches. Smaller circle has radius of 2 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?

Question

I give medallssss!!

Two gears are connected and are rotating simultaneously. The smaller gear has a radius of 2 inches, and the larger gear has a radius of 8 inches.

two circles touching at one point. Larger circle has radius of 8 inches. Smaller circle has radius of 2 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?

anonymous · Answer

guys please hellppp!!!!!!!!!!!!!

anonymous · Answer

attachment

anonymous · Answer

@phi  please

anonymous · Answer

@OOOPS  can you help me?

anonymous · Answer

@Callisto

anonymous · Answer

@ganeshie8  can you help me in this one ?

phi · Answer

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?

First,  what is the circumference of the smaller gear?

anonymous · Answer

what is the formula?

phi · Answer

It is a *very* famous formula
C= 2 pi r

anonymous · Answer

50.3

anonymous · Answer

sorry that's for the bigger one

anonymous · Answer

it's 12.6

phi · Answer

that is the circumference of the big gear.

the C for the smaller gear is 2*pi * 2  =  4 pi  (I would leave it that way)
C for the big gear    is 2 * pi *8 = 16 pi

now what fraction of the little gear to the big gear?   When the little gear turns once around, what fraction of the big gear did we turn ?

anonymous · Answer

16 pi /4 pi

phi · Answer

which simplifies to 4/1  or 4
that means  the big gear is 4 times bigger than the little gear

I would write it the "other way"
¼   which means   the big gear turns ¼ of the way around when the little gear turns once

phi · Answer

What is the angle measure, in degrees ?

in other words, if we turn ¼ of the way around, what is that in degrees ?
(remember all the way round is 360º)

anonymous · Answer

90 degrees ------> 360 * 1/4

phi · Answer

yes.

care to tackle 
Part 2: How many rotations will the smaller gear make during one complete rotation of the larger gear?

anonymous · Answer

now  we have to divide the circumference of the bigger one by the circunference of the smaller one?

anonymous · Answer

16 pi / 4 pi and we will get 4 pi

phi · Answer

the pi's cancel

anonymous · Answer

oh yeah! so it would be 4 rotations?

phi · Answer

yes

anonymous · Answer

Okay!!! thank you @phi I really appreciate it . :)

phi · Answer

yw

anonymous · Answer

;)