To find the height of the candle, we start by determining the dimensions of the cylindrical candle. The given information is:
- The distance from the wick (located in the center) to the edge of the candle (the radius, \(r\)) is \(2\frac{1}{4}\) inches, which is equivalent to \(2.25\) inches.
- The volume of the wax used in the candle (\(V\)) is approximately \(159\) cubic inches.
The formula for the volume of a cylinder is:
\[ V = \pi r^2 h \]
where:
- \(V\) is the volume,
- \(r\) is the radius,
- \(h\) is the height.
Substituting the known values into the formula:
\[ 159 = \pi (2.25)^2 h \]
Calculating \( (2.25)^2 \):
\[ (2.25)^2 = 5.0625 \]
Now substituting that back into the volume formula:
\[ 159 = \pi (5.0625) h \]
Now, solving for \(h\):
\[ h = \frac{159}{\pi \cdot 5.0625} \]
Calculating \(\pi \cdot 5.0625\):
\[ \pi \cdot 5.0625 \approx 15.903 \]
Now substituting that value into the equation:
\[ h \approx \frac{159}{15.903} \approx 9.99 \]
Rounding to the nearest whole number gives us:
\[ h \approx 10 \]
Therefore, the approximate height of the candle is 10 inches.
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