Question

Find the amount of water displaced by a solid spherical ball of diameter $4.2cm$, when it is completely immersed in water.

Answer 1

Evaluate the volume of the given sphere

We know that volume of sphere is $\frac{4}{3}{\mathrm{\pi r}}^3$

Given, diameter $4.2cm$. So, radius will be $2.1cm$

As the spherical object is completely immersed in water, a large amount of water will be displaced. The displaced water will be equal to the volume of the object. So, the volume will be,

$$\begin{gathered} \Rightarrow V=\frac{4}{3}{\mathrm{\pi r}}^3 \\ \Rightarrow \mathrm{V}=\frac{4}{3}\times \frac{22}{7}\times {(2.1)}^3 \\ \Rightarrow \mathrm{V}=38.808{\mathrm{cm}}^3 \end{gathered}$$

Therefore, the water displaced by the spherical object is $38.808c{m}^3$.