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{
  "topic": "tetrahedron-circumradius",
  "input_types": [
    "float"
  ],
  "input_labels": [
    "s"
  ],
  "input_values": [
    "8"
  ],
  "input_units": [
    "units"
  ],
  "input_descriptions": [
    "length of side"
  ],
  "examples": [
    {
      "s": 20
    },
    {
      "s": 1
    }
  ],
  "type": "Calculate",
  "title": "Tetrahedron Circumradius",
  "category": "Geometry",
  "shape": "Tetrahedron",
  "formula_mathjax": "\\( \\frac{ s \\sqrt{6} }{4} \\)",
  "formula_mathjax_sub": "\\( \\frac{ s \\times \\sqrt{6} }{4} \\)",
  "formula": "( s * Math.sqrt(6) / 4 )",
  "op_label": "Circumradius",
  "output_unit": "units",
  "description": "The Tetrahedron Circumradius calculator calculates the radius of the circumcircle surrounding the tetrahedron by taking the length of its side as input.",
  "explanation": "The circumradius of a tetrahedron is the radius of the sphere that circumscribes the tetrahedron, meaning it is the distance from the center of the tetrahedron to any of its vertices.",
  "examples_data": "<h2>Examples</h2><p>The following examples cover how to calcualte the Circumradius when length of side is given.</p><div class=\"example\"><h3 class=\"question\"><span class=\"example_n\">1.</span> What is the Circumradius of Tetrahedron whose length of side is 20 units?</h3><h4 class=\"answer\">Answer</h4><p>Given:</p><ul><li>length of side, s = 20 units</ul><p>The formula to find the Circumradius of a Tetrahedron is:</p><p class=\"tabspace\">R = \\( \\frac{ s \\sqrt{6} }{4} \\)</p><p>Substitute given values in the above formula.</p><p class=\"tabspace\">R = \\( \\frac{20\\times \\sqrt{6} }{4} \\)</p><p class=\"tabspace\">R = 12.25 units</p><p class=\"tabspace answer\">∴ Circumradius, R = 12.25 units</p></div><div class=\"example\"><h3 class=\"question\"><span class=\"example_n\">2.</span> What is the Circumradius of Tetrahedron whose length of side is 1 units?</h3><h4 class=\"answer\">Answer</h4><p>Given:</p><ul><li>length of side, s = 1 units</ul><p>The formula to find the Circumradius of a Tetrahedron is:</p><p class=\"tabspace\">R = \\( \\frac{ s \\sqrt{6} }{4} \\)</p><p>Substitute given values in the above formula.</p><p class=\"tabspace\">R = \\( \\frac{1\\times \\sqrt{6} }{4} \\)</p><p class=\"tabspace\">R = 0.61 units</p><p class=\"tabspace answer\">∴ Circumradius, R = 0.61 units</p></div>",
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}