Question

The speedometer needle in a car is 2.5 inches long. When accelerating from 0 to 60 miles per hour the needle

sweeps out an arc of 130°. What is the arc length traveled by the needle? Round your answer to the nearest
hundredth.

Answer 1

The arc length traveled by the needle is 7.0904
`in^(2)`

Explanation:

Step 1

In the above question are given that

The speedometer needle in a car is 2.5 inches long

The needle sweeps out an arc of 130°.

Let r be the length of the speedometer needle,So

r=2.5

m∠C=130°

Step 2

The formula for determining the area of the sector is

A=
`(m)/(360)`*
`\pi r^(2)`

Where,the central angle is m°

and The radius is r

Substituting the value of m and r from the step 1 in the below equation we get

A=
`(130)/(360)`*
`\pi *2.5^(2)`

A= 0.3611*
`\pi`*6.5=7.0904
`in^(2)`

Hence the value of the Area of the sector is = 7.0904
`in^(2)`

Step 3

So, the arc length traveled by the needle 7.0904
`in^(2)`