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    Question

    Determine the volume of a cone with a curved surface

    area of 180 cm² and a radius of 6 cm. (Assume π = 3 for calculations.)
    A 320 cm² Correct Answer Incorrect Answer
    B 255 cm² Correct Answer Incorrect Answer
    C 288 cm² Correct Answer Incorrect Answer
    D 258 cm² Correct Answer Incorrect Answer
    E none of these Correct Answer Incorrect Answer

    Solution

    Let the slant height of the cone be ‘l’ cm. Curved surface area of the cone = π × r × l = 180 3 × 6 × I = 180 I = 10 cm Let height of the cone be ‘h’ cm. According to Pythagoras theorem: r2 + h2 = l2  62 + h2 = 102 h2 = 100 – 36 h = √64 = 8 So the volume of the cone = 1/3 × π × r2 × h = 1/3 × 3 × 36 × 8 = 288 cm2

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