What is the ratio of the volume of cone $A$ to the volume of cone $B$? Express your answer as a common fraction.

volume of cone  A  =  $\frac13\cdot\pi\cdot14.8^2\cdot28.3$

volume of cone  B  =  $\frac13\cdot\pi\cdot28.3^2\cdot14.8$

$\frac{\text{volume of cone A}}{\text{volume of cone B}}\,=\,\frac{\frac13\cdot\pi\cdot14.8^2\cdot28.3}{\frac13\cdot\pi\cdot28.3^2\cdot14.8}\,=\,\frac{14.8^2\cdot28.3}{28.3^2\cdot14.8}\,=\,\frac{14.8}{28.3}\,=\,\frac{148}{283}$