To find the height of the cylindrical candle, we can use the formula for the volume of a cylinder, which is given by:
\[ V = \pi r^2 h \]
where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height of the cylinder.
Given:
- The volume of the wax (V) = 159 in³
- The distance from the wick to the edge of the candle = \( 2 \frac{1}{4} \) inches
First, let's convert \( 2 \frac{1}{4} \) inches into an improper fraction or decimal:
\[ 2 \frac{1}{4} = 2 + \frac{1}{4} = \frac{8}{4} + \frac{1}{4} = \frac{9}{4} \text{ inches} = 2.25 \text{ inches} \]
This distance represents the radius of the candle, so:
\[ r = 2.25 \text{ inches} \]
Now, substituting the radius into the volume formula:
\[ V = \pi (2.25)^2 h \]
Calculating \( (2.25)^2 \):
\[ (2.25)^2 = 5.0625 \]
Now substituting back into the equation for volume:
\[ 159 = \pi (5.0625) h \]
Now, solving for \( h \):
\[ h = \frac{159}{\pi (5.0625)} \]
Using \( \pi \approx 3.14159 \):
\[ h \approx \frac{159}{3.14159 \times 5.0625} \] \[ h \approx \frac{159}{15.9031} \approx 10.0 \]
Thus, the height of the candle to the nearest whole number is:
\[ \text{The candle's height is approximately } 10 \text{ inches.} \]