{
  "problem": "A circle has a sector with area $\\dfrac{125}{6}\\pi$ and central angle $300^\\circ$. What is the area of the circle? ${25\\pi}$ $\\color{#9D38BD}{300^\\circ}$ ${\\dfrac{125}{6}\\pi}$",
  "hints": [
    "The ratio between the sector's central angle",
    "$\\theta$",
    "and",
    "$360^\\circ$",
    "is equal to the ratio between the sector's area,",
    "$A_s$",
    ", and the whole circle's area,",
    "$A_c$",
    "$\\dfrac{\\theta}{360^\\circ} = \\dfrac{A_s}{A_c}$",
    "$\\dfrac{300^\\circ}{360^\\circ} = \\dfrac{125}{6}\\pi \\div A_c$",
    "$\\dfrac{5}{6} = \\dfrac{125}{6}\\pi \\div A_c$",
    "$A_c \\times \\dfrac{5}{6} = \\dfrac{125}{6}\\pi$",
    "$A_c = \\dfrac{125}{6}\\pi \\times \\dfrac{6}{5}$",
    "$A_c = 25\\pi$"
  ]
}
{'source': 'AMPS', 'file': 'amps/khan/462/1608183205.json'}