To find the height of the candle, we will first determine the radius of the candle and then use the volume formula for a cylinder to find the height.
-
Determine the radius of the candle:
- The distance of the wick to the edge of the candle is 2 inches, which means the radius \( r \) of the candle is: \[ r = 2 \text{ inches} \]
-
Volume formula for a cylinder:
- The volume \( V \) of a cylinder is given by the formula: \[ V = \pi r^2 h \] Where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height.
-
Substitute the known values:
- We know that the volume \( V \) is approximately 159 in³ and \( r = 2 \) inches. Substituting these into the volume formula gives: \[ 159 = \pi (2^2) h \] \[ 159 = \pi (4) h \] \[ 159 = 4\pi h \]
-
Solve for \( h \):
- Rearranging the equation for \( h \): \[ h = \frac{159}{4\pi} \]
-
Calculate \( h \):
- Using \( \pi \approx 3.14 \): \[ h \approx \frac{159}{4 \times 3.14} \approx \frac{159}{12.56} \approx 12.66 \]
-
Rounding to the nearest whole number:
- Rounding 12.66 gives approximately 13 inches.
Given that 13 inches is not among the options you've provided (1, 10, 22, 23), it seems that there may be a misunderstanding in the conditions or a possible error in the volume given or options.
The calculated height of the candle is approximately 12.66 inches, so none of the provided options is correct. If you have other data or options, please provide them for clarification. Otherwise, based on the data given, the correct height should be about 13 inches.