text: ×
  Calculus
  
  # Polar Equations - Area
  
  A cow is tied to one point of a silo of radius 30, with a rope of length $$30 \pi$$ which would allow it to reach the opposite end of the silo.
  
  What is the total area of the grass that the cow can graze on?
  
  Given the graph above of the polar equation $$r=4+3\sin \theta,$$ what is the area of the shaded region?
  
  Find the area enclosed by one loop of the $$4$$-petal flower defined by the parametric equation $$r=5\cos 2\theta.$$
  
  Find the area of the region that lies inside the circle $$r=27\sin \theta$$ and outside the cardioid $$r=9+9\sin \theta.$$
  
  Find the area of the region bounded by the curve defined by $r^2=5\sin 2\theta, r \geq 0, 0 \leq \theta \leq \frac{\pi}{2}.$
  
  ×
explanation: The document contains multiple math questions related to finding areas in polar coordinates. Each question asks for the area of a specific region defined by polar equations or parametric equations. There are no provided answers to these questions.
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: ×
  Calculus
  
  # Polar Equations - Area
  
  A cow is tied to one point of a silo of radius 30, with a rope of length $$30 \pi$$ which would allow it to reach the opposite end of the silo.
  
  What is the total area of the grass that the cow can graze on?
  
  Given the graph above of the polar equation $$r=4+3\sin \theta,$$ what is the area of the shaded region?
  
  Find the area enclosed by one loop of the $$4$$-petal flower defined by the parametric equation $$r=5\cos 2\theta.$$
  
  Find the area of the region that lies inside the circle $$r=27\sin \theta$$ and outside the cardioid $$r=9+9\sin \theta.$$
  
  Find the area of the region bounded by the curve defined by $r^2=5\sin 2\theta, r \geq 0, 0 \leq \theta \leq \frac{\pi}{2}.$
  
  ×
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains multiple math questions related to finding areas in polar coordinates. Each question asks for the area of a specific region defined by polar equations or parametric equations. There are no provided answers to these questions.
  
  Label: multiple-question