Q32 of 56 Page 13

A sphere of diameter 12 cm, is dropped in a right circular cylindrical vessel, partly filled with water. If the sphere is completely submerged in water, the water level in the cylindrical vessel rises by cm. Find the diameter of the cylindrical vessel.(CBSE 2016)

Let the radius of sphere be r = 12/2 = 6 cm


And radius of cylinder is R


Let h and H be heights of water before and after putting the ball in water


Given



Volume of ball = volume of cylinder after putting ball - volume of cylinder before putting ball





4(216) = 10R2


R2 = 86.4


R = 9.29 cm


Diameter of cylindrical vessel = 2R = 2(9.29)


= 19.58 cm

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