Question

A) The distance of the wick to the edge of a cylindrical candle is \(3\frac{3}{4}\) inches, and the
volume of the wax used in the candle is approximately 175 \(in^3\). Assuming the wick is located
in the center of the candle, find the height of the candle to the nearest whole number. (1 point)
The candle's height is approximately ?inches

Answer 1

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

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

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

First, we need to convert the distance of the wick to the edge of the candle \(3\frac{3}{4}\) inches into an improper fraction:

\[
3\frac{3}{4} = 3 + \frac{3}{4} = \frac{12}{4} + \frac{3}{4} = \frac{15}{4} \text{ inches}
\]

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

\[
r = \frac{15}{4} \text{ inches}
\]

Next, we can express the radius in decimal form for easier calculation:

\[
r = \frac{15}{4} = 3.75 \text{ inches}
\]

Now, we can calculate the area of the base of the candle:

\[
\pi r^2 = \pi \left(3.75\right)^2
\]

Calculating \(r^2\):

\[
(3.75)^2 = 14.0625
\]

Thus, the base area is:

\[
\pi r^2 = \pi \cdot 14.0625 \approx 44.157 \text{ (using } \pi \approx 3.14159\text{)}
\]

Now, we can plug this into the volume formula to solve for \(h\):

\[
175 = \pi (14.0625) h
\]

Solving for \(h\):

\[
h = \frac{175}{\pi \cdot 14.0625}
\]

Calculating:

\[
h \approx \frac{175}{44.157} \approx 3.96
\]

Rounding to the nearest whole number, the height of the candle is:

\[
\boxed{4} \text{ inches}
\]