Question

150 spherical marbles, each of diameter 1.4 cm are dropped in a cylindrical vessel of diameter 7 cm containing some wate, which are completely immersed in water. Find the rise in the level of water in the vessel.

Answer 1

diameter of marble = 1.4 cm

radius of marble = 0.7 cm

number of marbles = 150

diameter of cylinder = 7cm

radius of cylinder = 3.5cm
Let the height of the water raised when 150 spheres are dropped in the vessel.

volume of 150 marbles = volume of water raised by height 'h' inside the vessel

$150\times \frac{4}{3}\times \pi \times {0.7}^3=\pi \times {3.5}^2\times h$

$[Since,Volumeofsphere=\frac{4}{3}\pi r^{3}andVolumeofcylinder=\pi r^{2}h]$

$50\times 4\times {0.7}^3={3.5}^2\times h$

$200\times 0.343=12.25\times h$

$h=\frac{68.6}{12.25}$

$h=5.6cm$

Height of water raised(h) = 5.6 cm