1. In the circle rearrangement experiment, as the number of sectors $n$ increases, what shape does the rearranged figure increasingly resemble?
- A. Triangle
- B. Trapezoid
- C. Rectangle
- D. Square
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Circle Area Formula Quiz
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In the circle rearrangement experiment, as the number of sectors n increases, what shape does the rearranged figure increasingly resemble?
Circle Area Formula Quiz - Quiz Questions
Test your understanding of the 'Rearrangement' limit concept and the derivation of the circle area formula.
2. What geometric quantity of the circle corresponds to the 'height' of the approximate rectangle?
- A. Diameter (d)
- B. Radius (r)
- C. Circumference (C)
- D. Chord Length
3. What is the 'width' of the rearranged rectangle equal to?
- A. Circumference (C)
- B. Half the Circumference ($\pi r$)
- C. Diameter (d)
- D. Radius (r)
4. Based on the derived formula $Area = \text{Width} \times \text{Height}$, what is the formula for the area of a circle?
- A. $2\pi r$
- B. $\pi r^2$
- C. $2\pi r^2$
- D. $\pi^2 r$
5. If the radius of a circle is $r=10$ and we take $\pi=3.14$, what is its area?
- A. 31.4
- B. 62.8
- C. 314
- D. 100
6. If we don't change the radius but cut the circle into more sectors (e.g., increasing from 16 to 64), what happens to the area of the rearranged figure?
- A. Increases
- B. Decreases
- C. Remains unchanged
- D. Cannot be determined
7. If the radius of the circle is doubled, how many times larger does the area become?
- A. 2 times
- B. 4 times
- C. 8 times
- D. Unchanged
8. Why do we use the concept of 'limit' ($n \to \infty$)?
- A. Because computers can't handle large numbers
- B. To make the shape look better
- C. Because only with infinite cutting does the rearranged shape strictly equal a rectangle, eliminating error
- D. Because ancients liked complex math