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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
Given, diameter of a marble = 1.4 cm
∴ Radius of marble = `1.4/2` = 0.7 cm
So, volume of one marble
= `4/3 pi(0.7)^3`
= `4/3 pi xx 0.343`
= `1.372/3 pi "cm"^3`
Also, given diameter of beaker = 7 cm
∴ Radius of beaker = `7/2` = 3.5 cm
Height of water level raised = 5.6 cm
∴ Volume of the raised water in beaker
= π(3.5)2 × 5.6
= 68.6π cm3
Now, required number of marbles
= `"Volume of the raised water in beaker"/"Volume of one spherical marble"`
= `(68.6 pi)/(1.372 pi) xx 3`
= 150
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