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प्रश्न
150 spherical marbles, each of diameter 1.4 cm, are dropped in a cylindrical vessel of diameter 7 cm containing some water, which are completely immersed in water. Find the rise in the level of water in the vessel.
उत्तर
We have,
the radius of spherical marble, `"r" = 1.4/2 = 0.7 "cm"` and
the radius of the cylindrical vessel, `"R"=7/2 "cm" = 3.5 "cm"`
Let the rise in the level of water rised in the vessel be H.
Now,
Volume of water rised in the cylindrical vessel = Volume of 150 spherical marbles
`rArr pi"R"^2"H" = 150xx4/3 pir^3`
⇒ R2H = 200r3
⇒ 3.5 × 3.5 × H = 200 × 0.7 × 0.7× 0.7
`rArr "H" = (200xx0.7xx0.7xx0.7)/(3.5xx3.5)`
∴ H = 5.6 cm
So, the rise in the level of water in the vessel is 5.6 cm.
Disclaimer: The diameter of the spherical marbles should be 1.4 cm instead 14 cm. The has been corrected above.
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