Question

A carnival ride is in the shape of a wheel with a radius of 25 feet. The wheel has 20 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. You must show all work and calculations to receive credit. (10 points)

Answer 1

Centre angle will be 360° as its totally a circle.

• radius=r=25ft

Angle between two cars=360/20=18°

• Arc length=L

$\\ \sf\longmapsto L=\dfrac{\theta}{360}(2\pi r)$

$\\ \sf\longmapsto L=\dfrac{18}{360}(2\pi(25))$

$\\ \sf\longmapsto L=\dfrac{1}{20}(50\pi)$

$\\ \sf\longmapsto L=2.5\pi ft$

Now

Area be A

$\\ \sf\longmapsto A=\dfrac{1}{2}Lr^2$

$\\ \sf\longmapsto A=\dfrac{1}{2}(2.5\pi)(25)^2$

$\\ \sf\longmapsto A=625(2.5)\pi\dfrac{1}{2}$

$\\ \sf\longmapsto A=1562.5\pi/2$

$\\ \sf\longmapsto A=781\pi ft^2=$