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. [CBSE 2014]

Answer 1

Let the rise in the level of water in the vessel be h cm.
Now, Volume of 150 spherical marbles = Volume of water displaced in the vessel

$$\begin{gathered} \Rightarrow 150\times \frac{4}{3}\times \frac{22}{7}\times {\left(\frac{1.4}{2}\right)}^3=\frac{22}{7}\times {\left(\frac{7}{2}\right)}^2\times h \\ \Rightarrow 200\times {\left(0.7\right)}^3={\left(\frac{7}{2}\right)}^2\times h \\ \Rightarrow h=5.6\mathrm{cm} \end{gathered}$$