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Deepak Bora
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Marbles of diameter 1.4 cm are dropped into a cylindrical beaker of diameter 7 cm, containing some water. Find the number of marbles that should be dropped into the beaker so that the water level rises by 5.6 cm.

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Problem from RS Aggarwal book, problem number 30, page number 812, exercise 17B, chapter volume and surface area of solid.
Chapter Mensuration

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  1. solution

    given data,

    Diameter of each marble = 1.4 cm

    Radius of each marble = 0.7 cm

    Volume of each marble = [4/3] πr³

    = [4/3] π[0.7]³

    The water rises as a cylindrical column.

    Volume of cylindrical column filled with water = πr²h

    = π 2² ×5. 6

    Total number of marbles = Volume of cylindrical water column/Volume of marble

    = [ π 2² ×5. 6] / [ [4/3] π[0.7]³ ]

    = 150

    ∴ Total number of marbles are 150

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