What is the ratio of the volume of cone $A$ to the volume of cone $B$? Express your answer as a common fraction.
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volume of cone A = \(\frac13\cdot\pi\cdot14.8^2\cdot28.3\)
volume of cone B = \(\frac13\cdot\pi\cdot28.3^2\cdot14.8\)
\(\frac{\text{volume of cone A}}{\text{volume of cone B}}\,=\,\frac{\frac13\cdot\pi\cdot14.8^2\cdot28.3}{\frac13\cdot\pi\cdot28.3^2\cdot14.8}\,=\,\frac{14.8^2\cdot28.3}{28.3^2\cdot14.8}\,=\,\frac{14.8}{28.3}\,=\,\frac{148}{283}\)
volume of cone A = \(\frac13\cdot\pi\cdot14.8^2\cdot28.3\)
volume of cone B = \(\frac13\cdot\pi\cdot28.3^2\cdot14.8\)
\(\frac{\text{volume of cone A}}{\text{volume of cone B}}\,=\,\frac{\frac13\cdot\pi\cdot14.8^2\cdot28.3}{\frac13\cdot\pi\cdot28.3^2\cdot14.8}\,=\,\frac{14.8^2\cdot28.3}{28.3^2\cdot14.8}\,=\,\frac{14.8}{28.3}\,=\,\frac{148}{283}\)