What is the ratio of the volume of cone $A$ to the volume of cone $B$? Express your answer as a common fraction. [asy]
size(260);
draw(ellipse((0,0),14.8,6),S);
label("Cone $A$", (0,-6), S);
draw((0,28.3)--(0,0),dashed);
label("$28.3$",(0,14),SW);
draw((-14.8,0)--(0,28.3)--(14.8,0));
draw("$14.8$",(-14.8,0)--(0,0),N,dashed);
draw(ellipse((50,0),28.3,6),S);
label("Cone $B$", (50,-6), S);
draw((21.7,0)--(50,14.8)--(78.3,0));
draw("$14.8$",(50,14.8)--(50,0),W,dashed);
draw("$28.3$", (21.7,0)--(50,0),N,dashed);
[/asy]
Let $x = 14.8$ and $y = 28.3$.  Then the volume of cone $A$ is \[\frac{1}{3} \pi x^2 y,\] and the volume of cone $B$ is \[\frac{1}{3} \pi y^2 x,\] so the desired ratio is \[\frac{\frac{1}{3} \pi x^2 y}{\frac{1}{3} \pi xy^2} = \frac{x}{y} = \frac{14.8}{28.3} = \boxed{\frac{148}{283}}.\]
\frac{148}{283}
Level 4
Geometry
Problem: What is the ratio of the volume of cone $A$ to the volume of cone $B$? Express your answer as a common fraction. [asy]
size(260);
draw(ellipse((0,0),14.8,6),S);
label("Cone $A$", (0,-6), S);
draw((0,28.3)--(0,0),dashed);
label("$28.3$",(0,14),SW);
draw((-14.8,0)--(0,28.3)--(14.8,0));
draw("$14.8$",(-14.8,0)--(0,0),N,dashed);
draw(ellipse((50,0),28.3,6),S);
label("Cone $B$", (50,-6), S);
draw((21.7,0)--(50,14.8)--(78.3,0));
draw("$14.8$",(50,14.8)--(50,0),W,dashed);
draw("$28.3$", (21.7,0)--(50,0),N,dashed);
[/asy]
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To find the ratio of the volumes of cone A and cone B, we first need to recall the formula for the volume of a cone, which is given by V = (1/3)πr²h, where r is the radius and h is the height. 

For cone A, the height is 28.3 and the radius is 14.8. We calculate the volume of cone A as follows:
V_A = (1/3)π(14.8)²(28.3).

Next, we calculate the volume of cone B. The height of cone B is 14.8 and the radius is 28.3. Thus, the volume of cone B is:
V_B = (1/3)π(28.3)²(14.8).

Now, we need to find the ratio of the volumes V_A to V_B:
Ratio = V_A / V_B = [(1/3)π(14.8)²(28.3)] / [(1/3)π(28.3)²(14.8)].

The (1/3)π terms cancel out, simplifying the ratio to:
Ratio = (14.8)²(28.3) / (28.3)²(14.8).

This further simplifies to:
Ratio = (14.8 / 28.3).

To express this as a common fraction, we calculate:
14.8 / 28.3 = 148 / 283 after multiplying both the numerator and denominator by 10 to eliminate the decimal.

Thus, the final answer is the ratio of the volumes of cone A to cone B, which is expressed as the common fraction $\frac{148}{283}$.<|END_OF_LATENT|> The final answer is $\frac{148}{283}$.