A cylinder is placed inside a cube so that it stands upright when the cube rests on one of its faces. If the volume of the cube is 16, what is the maximum possible volume of the cylinder that fits inside the cube as described?

Correct.
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Now that you have the maximum height and radius, __Plug In__ $$\sqrt[3]{2}$$ for $$r$$ and $$2 \sqrt[3]{2}$$ for $$H$$.
>$$V = \pi r^2\cdot H$$
>$$\ \ = \pi (\sqrt[3]{2})^2\cdot (2\sqrt[3]{2}) $$
Rewrite the roots as fractional exponents.
>$$V= \pi \cdot 2^{\frac{2}{3}} \cdot 2\cdot2^{\frac{1}{3}}$$
Finally, simplify according to the rule for multiplying powers with the same base.
>$$V= 2\pi\cdot 2^{\frac{2}{3}+\frac{1}{3}}$$
>$$\ \ = 2\pi\cdot 2^1$$
>$$\ \ = 4\pi$$

Incorrect.
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$$ \frac{16}{\pi}$$

$$2\pi$$

$$8$$

$$4\pi$$

$$8\pi$$