<s>[INST] Find the diameter of iron ball. 
Iron weights $8$ times the weight of oak, Find the diameter of an iron ball whose weight is equal to that of a ball of oak $18$ cm in diameter. 

$a)\quad   4.5\quad  cm \\\color{green}{b)\quad   9 \quad  cm}\\c)\quad   12\quad   cm\\d) \quad  15 \quad  cm$
I tried 
$\dfrac43\times \pi\times (\dfrac{d}{2})^3 =8\times \dfrac43\times \pi\times (9)^3\\~\\
d=36\quad cm$
what is the mistake ?
 [/INST] Since iron weighs $8$ times what oak weighs, you need the iron ball to have $\frac{1}{8}$ the volume of the oak ball.
$$\begin{align}
  \frac{4}{3} \times \pi \times \left(\frac{d}{2}\right)^3 &=
  \color{red}{\frac{1}{8}} \times \frac{4}{3} \times \pi \times (9)^3  \\
  \frac{d^3}{8} &= \frac{1}{8} \times (9)^3  \\
  d^3 &= 9^3 \\
  d &= 9
\end{align}$$
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