I understand how to get the central angle and the arc length, but I am having a little trouble with the area of a sector..

A carnival ride is in the shape of a wheel with a radius of 15 feet. The wheel has 24 cars attached to the center of the wheel. What is the central angle, arc length, and area of a sector between any two cars? Round answers to the nearest hundredth if applicable.

Question

I understand how to get the central angle and the arc length, but I am having a little trouble with the area of a sector..



A carnival ride is in the shape of a wheel with a radius of 15 feet. The wheel has 24 cars attached to the center of the wheel. What is the central angle, arc length, and area of a sector between any two cars? Round answers to the nearest hundredth if applicable.

anonymous · Answer

@hartnn

hartnn · Answer

Area of sector = (Central angle)/ 360 $\times\pi r^2 $

anonymous · Answer

to fine the central angle i need to take $$\frac{ 2\Pi }{ 24 }$$ right?

hartnn · Answer

yes :)
or if you need it in degrees, then 360/24

hartnn · Answer

Area of sector = (Central angle in degrees/ 360) ×πr^2

Area of sector = (Central angle in radians/ 2$\pi$) ×πr^2

anonymous · Answer

I got .26 for the central angle

hartnn · Answer

thats correct, then use this
Area of sector = (Central angle in radians/ 2π) ×πr^2

anonymous · Answer

29.25

hartnn · Answer

thats correct! :)

anonymous · Answer

Thank you so much!

hartnn · Answer

welcome ^_^