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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.
Solution
Given, diameter of spherical marble = 1.4 cm
∴ Radius = `1.4/2` = 0.7 cm.
Volume of one ball = `4/3pir^3`
= `4/3pi (0.7)^3 cm^3` ...(i)
Diameter of beaker = 7 cm
∴ Radius = `7/2` cm,
Height of water (h) = 5.6 cm
∴ Volume of water = πr2h
= `pi (7/2 xx 7/2 xx 5.6) cm^3`
∴ Required No of balls dropped
= `(pi xx 49 xx 56 xx 3)/(4 xx 10 xx 4pi xx (0.7)^3)`
= `(49 xx 56 xx 3 xx 10 xx 10 xx 10)/(4 xx 10 xx 7 xx 7 xx 7 xx 4)`
= 150
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