text: +0
  
  # help!
  
  0
  68
  3
  +862
  
  Find the area of the segment of the circle :)
  
  May 10, 2021
  
  #1
  +32833
  +1
  
  Calculate the entire area of the 60 degree arc then subtract the area of the equilateral triangle
  
  pi r^2  *  60 / 360   = 6 pi
  
  Area of eqil triangle    sqrt 3/ 4  * 6^2
  
  6 pi   -   sqrt 3  / 4   * 36 = 3.261 cm2
  
  May 10, 2021
  #2
  +862
  0
  
  Thank you!
  
  AnimalMaster  May 10, 2021
  #3
  +498
  +1
  
  The area of a sector of a circle given the radius (r) and the angle (a) is $\frac{a}{360} \cdot r^2 \cdot \pi$
  
  Here, the angle is $60$ and the radius is $6$ so we have $\frac{60}{360} \cdot 6^2 \pi= \frac{1}{6} \cdot 36 \pi = 6 \pi.$
  
  The area of the equilateral triangle: We first must know the height and width, which is 6, but we do not know the height(I am assuming we do not know the formula for the area of an equilateral triangle.) Let the height be $h.$ We have $(\frac{6}{2})^2 + h^2 = 6^2 \Rightarrow 9 + h^2 = 36 \Rightarrow h^2 = 27 = 3 \sqrt{3}.$
  
  The height is $3\sqrt{3},$ so the area is $\frac{1}{2} \cdot 3\sqrt{3} \cdot 6 = 9 \sqrt{3}.$
  
  The answer is the sector - equilateral triangle = $6 \pi - 9 \sqrt{3}.$
  
  May 10, 2021
explanation: The document contains a math question and multiple answers to the question. The question is about finding the area of a segment of a circle, and there are three responses providing different methods and solutions to the problem.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: +0
  
  # help!
  
  0
  68
  3
  +862
  
  Find the area of the segment of the circle :)
  
  May 10, 2021
  
  #1
  +32833
  +1
  
  Calculate the entire area of the 60 degree arc then subtract the area of the equilateral triangle
  
  pi r^2  *  60 / 360   = 6 pi
  
  Area of eqil triangle    sqrt 3/ 4  * 6^2
  
  6 pi   -   sqrt 3  / 4   * 36 = 3.261 cm2
  
  May 10, 2021
  #2
  +862
  0
  
  Thank you!
  
  AnimalMaster  May 10, 2021
  #3
  +498
  +1
  
  The area of a sector of a circle given the radius (r) and the angle (a) is $\frac{a}{360} \cdot r^2 \cdot \pi$
  
  Here, the angle is $60$ and the radius is $6$ so we have $\frac{60}{360} \cdot 6^2 \pi= \frac{1}{6} \cdot 36 \pi = 6 \pi.$
  
  The area of the equilateral triangle: We first must know the height and width, which is 6, but we do not know the height(I am assuming we do not know the formula for the area of an equilateral triangle.) Let the height be $h.$ We have $(\frac{6}{2})^2 + h^2 = 6^2 \Rightarrow 9 + h^2 = 36 \Rightarrow h^2 = 27 = 3 \sqrt{3}.$
  
  The height is $3\sqrt{3},$ so the area is $\frac{1}{2} \cdot 3\sqrt{3} \cdot 6 = 9 \sqrt{3}.$
  
  The answer is the sector - equilateral triangle = $6 \pi - 9 \sqrt{3}.$
  
  May 10, 2021
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a math question and multiple answers to the question. The question is about finding the area of a segment of a circle, and there are three responses providing different methods and solutions to the problem.
  
  Label: multiple-question-and-answer