Question

A Ferris wheel has a radius of 70 feet. Two particular cars are located such that the central angle between them is 135º. To the nearest tenth, what is the measure of the intercepted arc between those two cars on the Ferris wheel? a. 29.7 feet b. 9,450.0 feet c. 439.8 feet d. 164.9 feet

Answer 1

Option D

The measure of the intercepted arc between those two cars on the Ferris wheel is 164.9 feet

Solution:

Given that Ferris wheel has a radius of 70 feet

Two particular cars are located such that the central angle between them is 135 degrees

To find: Arc length

From given question,

radius = r = 70 feet

central angle =
`\theta` = 135 degrees

The length of an arc, l, given the central angle, θ, and the radius, r, is given by:

`l= (\theta)/(360) *2\pi r`

Where, "l" is the length of arc and "r" is the radius and
`\pi = 3.14`

Substituting the given values we get,

`l = (135)/(360) * 2 * 3.14 * 70`

`l = 0.375 * 2 * 3.14 * 70\\\\l = 0.375 * 439.6\\\\l = 164.85 \approx 164.9`

Thus the length of arc is 164.9 feet