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Question

Spherical marbles of diameter 1.4 cm are dropped into beaker containing some water and are fully submerged. The diameter of the beaker is 7 cm. Find how many marbles have been dropped in it if the water rises by 5.6 cm ?

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Solution

Diameter of marble = 1.4 cm
radius = 1.4/2 = 0.7 cm
volume of 1 marble = 4 over 3 πr cubed equals 4 over 3 straight pi open parentheses 0.7 close parentheses cubed
let number of marbles required = n

base diameter of beaker = 7cm
radius = 7/2 = 3.5 cm
height rise in water = 5.6 cm

volume change = volume of n marbles
πr squared straight h equals straight n 4 over 3 straight pi left parenthesis 0.7 right parenthesis cubedleft parenthesis 3.5 right parenthesis squared 5.6 equals straight n 4 over 3 left parenthesis 0.7 right parenthesis cubedstraight n equals 150



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