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Correct. [[snippet]] 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. >$$V= 2\pi\cdot 2^{\frac{2}{3}+\frac{1}{3}}$$ >$$\ \ = 2\pi\cdot 2^1$$ >$$\ \ = 4\pi$$
$$\frac{16}{\pi}$$
$$2\pi$$
$$8$$
$$4\pi$$
$$8\pi$$