Solid spherical ball of radius 6 cm is melted and recast into 64 identical spherical marble. Find the radius of each marble.

Given,

Radius of larger metallic sphere (R) = 6 cm

Let radius of each smaller sphere be r cm.

Given,

A solid metallic sphere of radius 6 cm is melted and recast into 64 identical solid spheres.

∴ Volume of larger metallic sphere = 64 × Volume of smaller metallic sphere

$\Rightarrow \dfrac{4}{3}πR^3 = 64 \times \dfrac{4}{3}πr^3\\[1em] \Rightarrow R^3 = 64 \times r^3\\[1em] \Rightarrow 6^3 = 64 \times r^3\\[1em] \Rightarrow 216 = 64 \times r^3\\[1em] \Rightarrow r^3 = \dfrac{216}{64}\\[1em] \Rightarrow r = \sqrt[3]{\dfrac{216}{64}}\\[1em] \Rightarrow r = \dfrac{\sqrt[3]{216}}{\sqrt[3]{64}}\\[1em] \Rightarrow r = \dfrac{6}{4}\\[1em] \Rightarrow r = 1.5$

Hence, radius of each marble = 1.5 cm.