Question

The chain of a bicycle travels along the front and rear sprockets. The circumference of each sprocket is given. How long is the chain? Round to the hundredth.​

Answer 1

Answer:

35.61 ins.

Step-by-step explanation:

The length of the chain = 10 + 10 + the length of the arc of contact in small circle + the length of arc in  of the large  circle

= 10 + 10 + (160/360) * 12 + (186/360) * 20

= 35.61 ins.

Answer 2

   Length of the chain including both the chain sprockets will be 35.61 inches.

Circumference of the sector in a circle:

•   Circumference of a sector in a circle is given by the expression,

           $C=(\frac{\theta}{360^\circ} )(\text{Circumference of the small circle})$

           Here, r = Radius of the circle

                     θ = Angle at the center of a circle formed by the sector

Given in the question,

Circumference of the small circle = 12 in.

Circumference of the large circle = 20 in.

Circumference of the sector in small circle = $(\frac{160}{360} )(12)$

                                                                       = 5.33 in.

Circumference of the sector in large circle = $(\frac{185}{360} )(20)$

                                                                       = 10.28 in

Total length of the chain = 10 + (Circumference of the sector in small circle) + 10 + (Circumference of the sector in large circle)

= 10 + 5.33 + 10 + 10.28

= 35.61 in.

        Therefore, length of the chain will be 35.61 in.

Learn more about the circumference of the sector here,

https://brainly.com/question/14284772?referrer=searchResults