Thousand balls

We have to create a thousand balls from a sphere with a diameter of 1 m. What will be their radius?

Correct answer:

r =  5 cm

Step-by-step explanation:

$$\begin{gathered} D=1\text{ m}\to \text{ cm}=1\cdot 100\text{ cm}=100\text{ cm } \\ R=D\mathrm{/}2=100\mathrm{/}2=50\text{ cm } \\ n=1000 \\ {V}_1={\displaystyle \frac{4}{3}}\cdot \pi \cdot R^3={\displaystyle \frac{4}{3}}\cdot 3.1416\cdot 50^3\doteq 523598.7756{\text{cm}}^3 \\ {V}_2=V_1\mathrm{/}n=523598.7756\mathrm{/}1000\doteq 523.5988{\text{cm}}^3 \\ {V}_2={\displaystyle \frac{4}{3}}\cdot \pi \cdot r^3{\text{cm}}^3 \\ r=\sqrt[3]{{\displaystyle \frac{V_2\cdot 3}{4\pi }}}=\sqrt[3]{{\displaystyle \frac{523.5988\cdot 3}{4\cdot 3.1416}}}=5=5\text{ cm } \\ \text{ Verifying Solution: } \\ {r}_2=R\mathrm{/}{n}^{1\mathrm{/}3}=50\mathrm{/}\sqrt[3]{1000}=5\text{ cm } \\ {r}_2=r \end{gathered}$$

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