Clay balls

How many clay balls with a radius of 1 cm can be made from a ball of clay with a radius of 8 cm?

Correct answer:

n =  512

Step-by-step explanation:

$$\begin{gathered} R=8\text{ cm } \\ r=1\text{ cm } \\ {V}_1={\displaystyle \frac{4}{3}}\cdot \pi \cdot R^3={\displaystyle \frac{4}{3}}\cdot 3.1416\cdot 8^3\doteq 2144.6606{\text{cm}}^3 \\ {V}_2={\displaystyle \frac{4}{3}}\cdot \pi \cdot r^3={\displaystyle \frac{4}{3}}\cdot 3.1416\cdot 1^3\doteq 4.1888{\text{cm}}^3 \\ n=[V_1\mathrm{/}{V}_2]=[2144.6606\mathrm{/}4.1888]=512 \\ \text{ Verifying Solution: } \\ {n}_1=R^3\mathrm{/}{r}^3=8^3\mathrm{/}{1}^3=512 \end{gathered}$$

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