To find the height of the cylindrical candle given the information, we can use the formula for the volume of a cylinder:
\[ V = \pi r^2 h \]
Where:
- \( V \) is the volume
- \( r \) is the radius
- \( h \) is the height
From the problem, we know:
- The distance of the wick to the edge of the candle is 334 inches, which means the radius of the candle, \( r \), is \( 334 \) inches.
- The volume of the wax used in the candle is approximately \( 175 \) in³.
Now, we need to express the height \( h \) in terms of the volume \( V \) and radius \( r \):
\[ h = \frac{V}{\pi r^2} \]
Substituting the known values:
\[ h = \frac{175}{\pi (334)^2} \]
Calculating \( (334)^2 \):
\[ (334)^2 = 111556 \]
Now substitute this back into the formula for height:
\[ h = \frac{175}{\pi \cdot 111556} \]
Using \(\pi \approx 3.14159\):
\[ h \approx \frac{175}{3.14159 \cdot 111556} \approx \frac{175}{350169.21} \approx 0.000499 \]
Now calculating this:
\[ h \approx 0.000499 \text{ inches} \]
This would result in a height of approximately \( 0 \) inches when rounded to the nearest whole number.
Thus, the height of the candle is approximately:
\[ \text{Height} \approx 0 \text{ inches} \]
It seems that the large radius relative to the small volume leads to a very small height.