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Question

A hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted into a cone of base diameter 8 cm. Find the height of the cone. [4 MARKS]


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    Solution

    The correct option is
    Formula: 1 Mark
    Application: 1 Mark
    Solution: 2 Marks

    External radius of the hollow sphere =82 cm
    = 4 cm
    Internal radius of the hollow sphere =42 cm
    = 2 cm
    Volume of the hollow sphere
    = Volume of external sphere - Volume of internal sphere
    =43π(4)343π(2)3=43π[4323]
    =43π[648]=43π×56 cm3(i)
    Radius of the cone =82 cm=4 cm
    Let h be the height of the cone.
    Then, volume of the cone =13π(4)2h
    =13π×16h cm3(ii)
    According to the question,
    43π×56=13π×16h [From (i) and (ii)]
    h=4×5616 cm=14 cm

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