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    Question

    Radius and height of a right circular cone are 36 cm and

    48 cm respectively. Cone is divided horizontally into three parts. Height of uppermost part is 12 cm and height of lowermost part is 16 cm. Find the ratio of volume of uppermost part, middle part and lowermost part respectively. (Use π = 3) BC = 36 cm, AP = 12 cm and BD = 16 cm 
    A 27:485:1216 Correct Answer Incorrect Answer
    B 3:48:122 Correct Answer Incorrect Answer
    C 28:486:1215 Correct Answer Incorrect Answer
    D 25:490:1201 Correct Answer Incorrect Answer
    E 26:484:1217 Correct Answer Incorrect Answer

    Solution

    PD = 48 - 12 - 16 = 20 cm
    ∆APQ ~ ∆ABC (by AA similarity)
    So, (PQ/BC) = (AP/AB)
    Or, PQ = (12/48) × 36 = 9 cm
    Again, ∆ADE ~ ∆ABC (by AA similarity)
    So, (DE/BC) = (AD/AB)
    Or, DE = (32/48) × 36 = 24 cm
    Volume of uppermost part = (1/3) × 3 × 9² × 12 = 972 cm³
    Volume of middle part = (1/3) × 3 × 24² × 32 - (1/3) × 3 × 9² × 12
    = 18432 - 972 = 17460 cm³
    Volume of lowermost part = (1/3) × 3 × 36² × 48 - (1/3) × 3 × 24² × 32
    = 62208 - 18432 = 43776 cm³
    Required ratio = 972:17460:43776 = 27:485:1216

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