A small ferris wheel, a student is riding a 20-m-diameter ferris wheel that is making 3 revolutions per minute. What is the area of the sector between 3 of the seats (3/8) of the wheel?

radius - 10 m

This has nothing to do with the speed. That is just given to confuse the student

Between three of the seats is also confusing because if there are 8 seats there is for example one at 0 degrees , one at 45 degrees and one at 90 degrees
so the area is 1/4, not 1/3 of the circle

1/4 of area of circle =(1/4)(pi r^2)

To find the area of the sector between 3 of the seats on a ferris wheel, you first need to calculate the angle of the sector.

Since the ferris wheel is making 3 revolutions per minute, it completes 3 x 360° = 1080° in one minute.

To convert this angle to radians, use the conversion factor: 1 revolution = 2π radians.

So, 1080° = (1080/360) x 2π = 6π radians.

The total angle of the ferris wheel is 2π radians since it is a complete circle.

To find the angle of the sector, multiply the total angle (2π) by the fraction representing 3/8 of the wheel:
Sector angle = (3/8) x 2π = 3π/4 radians.

The area of the sector is calculated using the formula:
Area = (Sector angle/Total angle) x πr^2.

In this case, the diameter of the ferris wheel is 20 meters, so the radius is 20/2 = 10 meters.

Substituting the values into the formula, we have:
Area = (3π/4) / (2π) x π(10)^2 = (3/8) x 100π = 75π square meters.

Therefore, the area of the sector between 3 of the seats (3/8 of the wheel) is 75π square meters, or approximately 235.62 square meters.