Question

A spherical steel ball of radius r is melted to make eight new identical balls. The radius of each new ball is _________.

Answer 1

Let the radius of each new ball be R.

∴ Volume of spherical steel ball = 8 × Volume of each new ball

$$\begin{gathered} \Rightarrow \frac{4}{3}\mathrm{\pi }{r}^3=8\times \frac{4}{3}\mathrm{\pi }{R}^3 \\ \Rightarrow R^3=\frac{r^3}{8}={\left(\frac{r}{2}\right)}^3 \\ \Rightarrow R=\frac{r}{2} \end{gathered}$$

A spherical steel ball of radius r is melted to make eight new identical balls. The radius of each new ball is $\underline{\frac{r}{2}}$.