Question

The height of a cylindrical candle is 5 inches. The volume of the wax used to make the candle is approximately 35 in³. Assuming the wick is located in the center of the candle, find the distance from the wick to the edge of the candle to the nearest tenth.

Answer 1

To find the distance from the wick to the edge of the 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 of the base, and \( h \) is the height.

We are given the following:

- Volume \( V = 35 \, \text{in}^3 \)
- Height \( h = 5 \, \text{in} \)

We can rearrange the formula to solve for the radius \( r \):

\[
r^2 = \frac{V}{\pi h}
\]

Substituting the known values into the equation:

\[
r^2 = \frac{35}{\pi \times 5}
\]

Calculating \( \pi \times 5 \):

\[
\pi \times 5 \approx 15.70796
\]

Now substituting that back into the equation:

\[
r^2 = \frac{35}{15.70796} \approx 2.228
\]

Now calculate \( r \):

\[
r \approx \sqrt{2.228} \approx 1.494
\]

Therefore, the radius \( r \) is approximately \( 1.494 \) inches.

The distance from the wick to the edge of the candle (which is the radius \( r \)) is:

\[
\text{Distance} \approx 1.5 \, \text{inches} \text{ (to the nearest tenth)}
\]

Thus, the distance from the wick to the edge of the candle is approximately **1.5 inches**.