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      Question

      The radius of a cone is 7 cm, and its height is 24 cm. A

      sphere is inscribed in the cone, touching the base and the curved surface. Find the radius of the sphere.
      A 5 cm Correct Answer Incorrect Answer
      B 6.72 cm Correct Answer Incorrect Answer
      C 7.55 cm Correct Answer Incorrect Answer
      D 8 cm Correct Answer Incorrect Answer

      Solution

      For an inscribed sphere in a cone, the radius of the sphere r is given by the formula: r = (r ├Ч h) / тИЪ(r┬▓ + h┬▓), where r is the radius of the coneтАЩs base, and h is its height. Substituting the values: r = (7 ├Ч 24) / тИЪ(7┬▓ + 24┬▓) = 168 / тИЪ(49 + 576) = 168 / 25 = 6.72 cm.

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