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Question
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.
Solution
Diameter of each marble = 1.4 cm
Radius of each marble = 0.7 cm
Volume of each marble `= 4/3pir^3 = 4/3pixx(0.7)^3 "cm"^3`
The water rises as a cylindrical column.
Volume of cylindrical column filled with water `= pir^2h =pi xx (7/2)^2 xx 5.6 "cm"^3`
Total number of marbles
`="Volume of cylindrical water column"/"Volume of marble" `
`= (pixx(7/2)^2 xx 5.6)/ (4/3pi xx (0.7)^3) `
`= (7xx7xx5.6xx3)/(2xx2xx4xx0.7xx0.7xx0.7)`
`=150`
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