The volume of a spherical ball is 2,000 cm³. What is the radius of the ball? (Take $\mathrm{\pi }=\frac{22}{7}, \sqrt[3]{42}=3.4 \mathrm{and} \sqrt[3]{11} =2.2$)

Volume of Sphere = $\frac{4}{3}{\mathrm{\pi r}}^3$

V = 2000 $c{m}^3$

Therefore,

$\mathrm{V} = \frac{4}{3}{\mathrm{\pi r}}^3$

$\Rightarrow 2000=\frac{4}{3}{\mathrm{\pi r}}^3$

$\Rightarrow 2000=\frac{4}{3}\times \frac{22}{7}\times {\mathrm{r}}^3$

$\Rightarrow {\mathrm{r}}^3=\frac{2000\times 21}{88}$

$\Rightarrow {\mathrm{r}}^3=\frac{42000}{88}$

$\Rightarrow {\mathrm{r}}^3=\frac{42000}{88}=\frac{5250}{11}$

$$\begin{gathered} \Rightarrow \mathrm{r}=\sqrt[3]{\frac{5250}{11}} \\ =\frac{5\sqrt[3]{42}}{\sqrt[3]{11}} \end{gathered}$$

$\Rightarrow \mathrm{r}=\frac{5\times 3.4}{2.2}$

$\Rightarrow \mathrm{r}=\frac{85}{11}$

$\Rightarrow \mathrm{r}=7.\stackrel{\mathrm{\_\_}}{72}$

$\Rightarrow \mathrm{r}\approx 7.7$

Hence, the radius is 7.7 cm.