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a sphere of diameter 6cm dropped …

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a sphere of diameter 6cm dropped in a right circular cylindrical vessel partly filled with water. The diameter of cylindrical vessel is 12cm. If the sphere is completely submereged in water, by how much the will the level of water rise in the cylindrical vessel?

    • Posted by Siddharth Singh 8 years, 10 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Naveen Sharma 8 years, 10 months ago

    Ans. Increased water level makes a Psuedo cylinder with height h which has equal volume to volume of the sphere

    Given : The Diameter of sphere = 6cm

    Radius of Sphere = 6/2 = 3cm

    Diameter of Cylindrical Vessel = 12cm

    Radius of Cylindrical Vessel = 12/2 = 6cm

    Volume of sphere = 43π r 3 = 43 π× 33 = 36π        ........(1)

    => Volume of Cylindrical vessel  = π r2 h = π 62 h = 36πh         .......(2)

    From (1) and (2)

    => 36πh = 36π

    => h = 1 cm

    Water level raise by 1 cm

    0Thank You

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