The arc length traveled by the needle is 7.0904[tex]in^{2}[/tex]
Step-by-step 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=[tex]\frac{m}{360}[/tex]*[tex]\pi r^{2}[/tex]
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=[tex]\frac{130}{360}[/tex]*[tex]\pi *2.5^{2}[/tex]
A= 0.3611*[tex]\pi[/tex]*6.5=7.0904 [tex]in^{2}[/tex]
Hence the value of the Area of the sector is = 7.0904 [tex]in^{2}[/tex]
Step 3
So, the arc length traveled by the needle 7.0904 [tex]in^{2}[/tex]
