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    Question

    A cone has a base radius of 6 cm and a height of 8 cm. A

    sphere is placed inside the cone such that it touches the base and the slant height of the cone. Find the radius of the sphere.
    A 2 cm Correct Answer Incorrect Answer
    B 3 cm Correct Answer Incorrect Answer
    C 4 cm Correct Answer Incorrect Answer
    D 5 cm Correct Answer Incorrect Answer

    Solution

    The radius of the sphere can be found using the formula: Radius of sphere = (r × h) / (√(r² + h²) + r) Where r = 6 cm (radius of cone) and h = 8 cm (height of cone). Radius = (6 × 8) / (√(6² + 8²) + 6) = 48 / (√(36 + 64) + 6) = 48 / (√100 + 6) = 48 / (10 + 6) = 48 / 16 = 3 cm Correct Option: b

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