Respuesta :
The length of an arc is given by (θ/360)2πr, where θ is the angle subtended by the arc at the center and r is the radius.
The angle θ in this case is 270°, while the radius is 7 feet, diameter is 14 feet
Thus the length of the of the cable will be;
=(270/360)× 22/7×14
= 0.75 × 44
= 33 feet
The angle θ in this case is 270°, while the radius is 7 feet, diameter is 14 feet
Thus the length of the of the cable will be;
=(270/360)× 22/7×14
= 0.75 × 44
= 33 feet
Answer:
The length of the cable is around 32.97 feet.
Step-by-step explanation:
The problem is about a circular sector, where the angle is 270° and the lenght of the subtended arc is the arc is the unknown variable.
The radius of the drive wheel is
[tex]r=\frac{d}{2}=\frac{14}{2}=7ft[/tex]
The central angle is 270°.
The length of the arc is
[tex]L=\frac{2\pi r \theta}{360\°}[/tex]
Replacing all values, we have
[tex]L=\frac{2(3.14)(7)(270\°)}{360\°}=\frac{11869.2}{360} \approx 32.97[/tex]
Thereofre, the length of the cable is around 32.97 feet.
