Question

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.

Answer 1

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.