The distance of the wick to the edge of a cylindrical candle is 2 1/4 inches, and the volume of wax used in the candle is approximately 159 in. Assuming the wick is located in the center of the candle, find the height of the candle to the nearest whole number What is the candles aproximate height in inches? (1 point) Ο 22 Ο 23 1,124 Ο 10

1 answer

To find the height of the cylindrical candle, we can use the formula for the volume of a cylinder, which is:

\[ V = \pi r^2 h \]

where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height.

Given:

  • The volume of the candle \( V \approx 159 \) cubic inches.
  • The distance from the wick to the edge of the candle is \( 2 \frac{1}{4} \) inches (which is \( 2.25 \) inches). This distance is the radius of the candle.

So, we can calculate the radius \( r \):

\[ r = 2.25 \text{ in} \]

Now we can substitute the values into the volume formula to solve for \( h \):

\[ 159 = \pi (2.25)^2 h \]

Calculating \( (2.25)^2 \):

\[ (2.25)^2 = 5.0625 \]

Now substituting it back into the formula:

\[ 159 = \pi (5.0625) h \]

\[ 159 = 15.9043 h \quad (\text{using } \pi \approx 3.14159) \]

Now, we solve for \( h \):

\[ h = \frac{159}{15.9043} \approx 10 \]

Thus, rounding to the nearest whole number, the candle's approximate height is:

\[ \boxed{10} \text{ inches} \]