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Marbles of diameter 1.4cm are dropped into a beaker containing some water and are fully submerged.The diameter of the beaker is 7cm.Find how many marbles

have been dropped in it if water rises by 56cm.



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Diameter of marble = 1.4 cm
radius = 1.4/2 = 0.7 cm
volume of 1 marble =  \frac{4}{3} \pi r^3 = \frac{4}{3} \times  \pi \times (0.7)^3
let number of marbles required = n

base diameter of beaker = 7cm
radius = 7/2 = 3.5 cm
height rise in water = 56 cm

volume change = volume of n marbles

 \pi r^2h=n \times \frac{4}{3} \times \pi \times (0.7)^3\\ \\n= \frac{ \pi \times 3.5^2 \times 56}{(4/3) \times  \pi \times 0.7^3} = \frac{3.5^2 \times 56 \times 3}{4 \times 0.7^3} =1500

So 1500 marbles should be dropped.
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