A cone is 8.4 cm high and the radius of its base is 2.1cm. It is melted and recast into a sphere, then the radius of the sphere is

Height , h$=$ 8.4 cm

Base radius, r$=$ 2.1 cm

Cone in melted and recast into the shape of a sphere,

$\therefore$ volume of cone $=$ Volume of sphere

$\frac{1}{3}\pi r^{2}h=\frac{4}{3}\pi R^3$

$\frac{1}{3}\times \pi \times 2.1\times 2.1\times 8.4=\frac{4}{3}\times \pi \times R^3$

$\frac{1}{3}\times \pi \times \frac{21}{10}\times \frac{21}{10}\times \frac{84}{10}\times \frac{3}{4}\times \frac{1}{\pi }=R^3$

${\left(\frac{21}{10}\right)}^3=R^3$

${\left(2.1\right)}^3=R^3$

$\therefore R=2.1$

$\therefore$ Radius of sphere, $R=$ 2.1 cm