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    Question

    Determine the volume of a cone with a curved surface

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

    Solution

    Let the slant height of the cone be тАШlтАЩ cm. Curved surface area of the cone = ╧А ├Ч r ├Ч l = 180 3 ├Ч 6 ├Ч I = 180 I = 10 cm Let height of the cone be тАШhтАЩ cm. According to Pythagoras theorem: r2 + h2 = l2┬а 62 + h2 = 102 h2 = 100 тАУ 36 h = тИЪ64 = 8 So the volume of the cone = 1/3 ├Ч ╧А ├Ч r2 ├Ч h = 1/3 ├Ч 3 ├Ч 36 ├Ч 8 = 288 cm2

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