What is the total area covered by the ferris wheel when it makes one revolution?
Understand the Problem
The question is asking for the total area covered by a ferris wheel when it makes one full revolution. The length from the center to the top is given as 20 meters, which implies the radius of the ferris wheel is 20 meters. The area of a circle can be calculated using the formula A = πr², where r is the radius.
Answer
The total area covered by the ferris wheel is approximately \( 1256 \, \text{square meters} \).
Answer for screen readers
The total area covered by the ferris wheel when it makes one full revolution is approximately ( 1256 , \text{square meters} ).
Steps to Solve
- Identify the radius of the ferris wheel
The problem states that the length from the center to the top is 20 meters. Therefore, the radius ( r ) of the ferris wheel is: $$ r = 20 , \text{meters} $$
- Use the area formula for a circle
The area ( A ) of a circle can be calculated using the formula: $$ A = \pi r^2 $$
- Substitute the radius into the area formula
Now substitute the value of the radius into the area formula: $$ A = \pi (20)^2 $$
- Calculate the area
Perform the calculation: $$ A = \pi (400) $$ This means: $$ A = 400\pi $$
- Provide the final answer
To get a numerical approximation, use ( \pi \approx 3.14 ): $$ A \approx 400 \times 3.14 = 1256 , \text{square meters} $$
The total area covered by the ferris wheel when it makes one full revolution is approximately ( 1256 , \text{square meters} ).
More Information
The area covered by a ferris wheel represents the space within the circular path it traces as it rotates. Since the ferris wheel is a circle, the use of the formula for the area of a circle is appropriate.
Tips
- Misunderstanding the radius: Some might confuse the diameter with the radius. Remember, the radius is half the diameter.
- Incorrect use of the formula: Ensure to square the radius and multiply by ( \pi ) properly.
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