Question

150 spherical marbles, each of diameter 14 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

Sol:
Diameter of the spherical marble = 1.4 cm
Radius of the marble = 0.7 cm
$Volumeofeachmarble=4/3\times \pi \times r^3=4/3\times \frac{22}{7}\times (0.7{)}^3=1.44$
Volume of 150 marbles = 1.44 × 150 = 216 $c{m}^3$
Let the rise in level of water in the cylindrical vessel = 'h' cm
Diameter of the vessel = 7 cm
Radius of the vessel = 3.5 cm
Volume of the increased level of the water = $\pi \times r^2\times h=\frac{22}{7}\times (3.5{)}^2\times h$
Volume of the increased level of the water = Volume of 150 marbles
$\frac{22}{7}\times (3.5{)}^2\times h=216$
⇒ h = 5.6 cm
Therefore, rise in level of water in the vessel = 5.6 cm.