question: The volume of a cylinder that fits exactly into a sphere is given by the formula:
  
  V=\frac{1}{4}\pi h\left(4r^2-h^2\right)
  
  where r is the radius of the sphere and h is the height of the cylinder.
  
  What is the radius of the sphere if the volume of the cylinder is 13.75\pi cm3 and the height of the cylinder is 5 cm?
query_wo: Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.
  Question: The volume of a cylinder that fits exactly into a sphere is given by the formula:
  
  V=\frac{1}{4}\pi h\left(4r^2-h^2\right)
  
  where r is the radius of the sphere and h is the height of the cylinder.
  
  What is the radius of the sphere if the volume of the cylinder is 13.75\pi cm3 and the height of the cylinder is 5 cm?
query_cot: Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.
  Question: The volume of a cylinder that fits exactly into a sphere is given by the formula:
  
  V=\frac{1}{4}\pi h\left(4r^2-h^2\right)
  
  where r is the radius of the sphere and h is the height of the cylinder.
  
  What is the radius of the sphere if the volume of the cylinder is 13.75\pi cm3 and the height of the cylinder is 5 cm?
question_for_eval: The volume of a cylinder that fits exactly into a sphere is given by the formula:
  
  V=\frac{1}{4}\pi h\left(4r^2-h^2\right)
  
  where r is the radius of the sphere and h is the height of the cylinder.
  
  What is the radius of the sphere if the volume of the cylinder is 13.75\pi cm3 and the height of the cylinder is 5 cm?