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Question
A cylindrical beaker of 7 cm diameter is partly filled with water. Determine the number of spherical marbles of diameter 1.4 cm that are to be submerged in it to raise the water level by 5.6 cm
Solution
Diameter of spherical marble = 1. 4 cm
Therefore, radius= 0.7 cm
Volume of one ball = `4/3pir^3`
= `4/3 xx pi xx (0.7)^3` cm3 ................(i)
Diameter of beaker = 7 cm
Therefore, radius = 3.5 cm
Height of water= 5.6 cm
Volume of water = `pir^2h`
= `pi xx (3.5)^2 xx 5.6` cm3 .......................(ii)
No. of balls dropped = `"Volume of water"/"Volume of ball"`
= `(pi xx (3.5)^2 xx 5.6)/(4/3 xx pi xx (0.7)^3)`
= `(3 xx (3.5)^2 xx 5.6)/(4 xx (0.7)^3)`
= 150
No. of balls dropped = 150
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