Question

Resolva essa conta:

$A_{lat}=\dfrac {3 \pi}{2} \cdot ( \sqrt[3]{256} ) ^{2}$

Answer 1

$\mathsf{A_{lat}=\dfrac{3\pi}{2}\cdot \big(\,^3\!\!\!\sqrt{256}\big)^2}\qquad\quad\textsf{(mas }\mathsf{256=2^8}\textsf{)}\\\\\\ \mathsf{A_{lat}=\dfrac{3\pi}{2}\cdot \big(\,^3\!\!\!\sqrt{2^8}\big)^{\!2}}\\\\\\ \mathsf{A_{lat}=\dfrac{3\pi}{2}\cdot \,^3\!\!\!\sqrt{(2^8)^2}}\\\\\\ \mathsf{A_{lat}=\dfrac{3\pi}{2}\cdot \,^3\!\!\!\sqrt{2^{8\,\cdot\,2}}}$

$\mathsf{A_{lat}=\dfrac{3\pi}{2}\cdot \,^3\!\!\!\sqrt{2^{16}}}\\\\\\ \mathsf{A_{lat}=\dfrac{3\pi}{2}\cdot \,^3\!\!\!\sqrt{2^{15+1}}}\\\\\\ \mathsf{A_{lat}=\dfrac{3\pi}{2}\cdot \,^3\!\!\!\sqrt{2^{15}\cdot 2^1}}\\\\\\ \mathsf{A_{lat}=\dfrac{3\pi}{2}\cdot \,^3\!\!\!\sqrt{2^{5\,\cdot\,3}\cdot 2^1}}\\\\\\ \mathsf{A_{lat}=\dfrac{3\pi}{2}\cdot \,^3\!\!\!\sqrt{2^{5\,\cdot\,3}}\cdot \,^3\!\!\!\sqrt{2}}$

$\mathsf{A_{lat}=\dfrac{3\pi}{2}\cdot \;^3\!\!\!\!\sqrt{(2^5)^3}\cdot \,^3\!\!\!\sqrt{2}}\\\\\\ \mathsf{A_{lat}=\dfrac{3\pi}{2}\cdot 2^5\cdot \,^3\!\!\!\sqrt{2}}\\\\\\ \mathsf{A_{lat}=3\pi\cdot 2^4\cdot \,^3\!\!\!\sqrt{2}}\\\\\\ \mathsf{A_{lat}=3\pi\cdot 16\cdot \,^3\!\!\!\sqrt{2}}\\\\\\ \boxed{\begin{array}{c}\mathsf{A_{lat}=48\pi\,^3\!\!\!\sqrt{2}} \end{array}}$


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