Question

PLEASE PLEASEEEEEEE HELPPPPPP!! 100 POINTSSSS :)

A Ferris wheel, called the Atlanta Skyview, recently opened in Centennial Olympic Park in the Atlanta, GA area. The diameter of this Atlanta attraction is 200 feet and has 42 gondolas evenly spaced out along the circle. Each sector starts and ends at the point at which the gondola is attached to the Ferris wheel circle.

Answer the following questions about this Ferris wheel. Be sure to show and explain all work for each problem.

a. Area of the wheel?

b. measure the central angle in degrees

c. Measure of a central angle in radians

d. Arc length between two gondolas

e. Area of each sector.

Answer 1

The area of the wheel is  31415.9 ft².

The Central angle in degrees is 34.29°

Measure of a central angle in radians is 0.5984 radians

How to calculate the area and central angle of a circle?

A) The image shows an example of this Ferris wheel.

We are given;

Diameter; d = 200 ft

Radius; r = 100 ft

Number of gondolas = 42

Area of the circle wheel = πr²

Area = π * 100²

Area = 31415.9 ft²

B) Now, the sum of angles in a circle is 360°.

Since there are 42 gondola's, then;

Each angle = 360/42 = 60/7°

The central angle will be an angle with its vertex at the center of a circle and with sides that are radii of the circle. From the image, we see that it covers approximately 4 gondola's. Thus;

Central angle = 4 * 60/7° = 34.29°

C) Central Angle in radians will be converted as 0.5984 rad.

D) Arc length between two gondolas is;

S = rθ

S = 100 * 0.5984

S = 59.84 radians

Read more about area and central angle at; https://brainly.com/question/12299316

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