A small ferris wheel: A student is riding a 20-m-diameter ferris wheel that is making three revolutions per minute. If there are eight equally spaced seats on the Ferris wheel, then what is the length of the arc between two adjacent seats?
clearly, that would be 20π/8
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?
clearly that would be 3/8 of the area of the entire circle.
I'm sure you know how to find the area of a circle...
On the other hand, 3 consecutive seats subtend only two angles, so the area should be 2/8 of the circle, no?
To find the length of the arc between two adjacent seats on the ferris wheel, we first need to determine the circumference of the ferris wheel.
The circumference of a circle is calculated using the formula C = πd, where C is the circumference and d is the diameter. Given that the diameter of the ferris wheel is 20 meters, we can calculate the circumference as follows:
C = π * 20
C ≈ 62.83 meters (rounded to two decimal places)
Now that we know the circumference of the ferris wheel, we need to find the length of the arc between two adjacent seats. Since there are eight equally spaced seats, we can divide the circumference by 8 to get the length of each arc:
Length of Arc = Circumference / Number of Seats
Length of Arc = 62.83 / 8
Length of Arc ≈ 7.85 meters (rounded to two decimal places)
Therefore, the length of the arc between two adjacent seats on the ferris wheel is approximately 7.85 meters.