Question
Question
The distance of the wick to the edge of a cylindrical candle is 214
inches, and the volume of wax used in the candle is approximately 159 in. 3
. Assuming the wick is located in the center of the candle, find the height of the candle to the nearest whole number.(8 points)
Responses
9 inches
9 inches
10 inches
10 inches
11 inches
11 inches
12 inches
12 inches
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The distance of the wick to the edge of a cylindrical candle is 214
inches, and the volume of wax used in the candle is approximately 159 in. 3
. Assuming the wick is located in the center of the candle, find the height of the candle to the nearest whole number.(8 points)
Responses
9 inches
9 inches
10 inches
10 inches
11 inches
11 inches
12 inches
12 inches
Skip to navigation
Answers
Answered by
GPT-4o mini
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 of the cylinder.
- \( r \) is the radius of the base.
- \( h \) is the height of the cylinder.
From the problem, we know:
- The distance from the wick (which is at the center) to the edge of the candle is the radius \( r = 214 \) inches.
- The volume \( V \) of the candle is approximately \( 159 \, \text{in}^3 \).
Substituting the known values into the volume formula:
\[
159 = \pi (214)^2 h
\]
Now we can solve for \( h \):
1. Calculate \( (214)^2 \):
\[
(214)^2 = 45796
\]
2. Substitute this back into the volume equation:
\[
159 = \pi (45796) h
\]
3. Rearranging to solve for \( h \):
\[
h = \frac{159}{\pi \times 45796}
\]
4. Now, calculate the denominator:
\[
\pi \times 45796 \approx 143785.18
\]
5. Now substitute back:
\[
h \approx \frac{159}{143785.18} \approx 0.00106 \text{ inches}
\]
Given that a radius of 214 inches is impractically large for such a small volume, it would be valuable to check the input values again. This indicates that either the radius or the volume might have been misunderstood or misstated.
However, we sought to find the height provided only with the above details. If the radius mentioned appears more reasonable, kindly verify the original candle dimensions, and we can calculate correctly from there.
But if the values stand, based on what was understood here, we find the height \( h \approx 0.00106 \) inches—definitely not aligning with typical height choices from your responses.
If you'd like a recalibration or re-evaluation of parameters, please share the correct figures!
\[
V = \pi r^2 h
\]
Where:
- \( V \) is the volume of the cylinder.
- \( r \) is the radius of the base.
- \( h \) is the height of the cylinder.
From the problem, we know:
- The distance from the wick (which is at the center) to the edge of the candle is the radius \( r = 214 \) inches.
- The volume \( V \) of the candle is approximately \( 159 \, \text{in}^3 \).
Substituting the known values into the volume formula:
\[
159 = \pi (214)^2 h
\]
Now we can solve for \( h \):
1. Calculate \( (214)^2 \):
\[
(214)^2 = 45796
\]
2. Substitute this back into the volume equation:
\[
159 = \pi (45796) h
\]
3. Rearranging to solve for \( h \):
\[
h = \frac{159}{\pi \times 45796}
\]
4. Now, calculate the denominator:
\[
\pi \times 45796 \approx 143785.18
\]
5. Now substitute back:
\[
h \approx \frac{159}{143785.18} \approx 0.00106 \text{ inches}
\]
Given that a radius of 214 inches is impractically large for such a small volume, it would be valuable to check the input values again. This indicates that either the radius or the volume might have been misunderstood or misstated.
However, we sought to find the height provided only with the above details. If the radius mentioned appears more reasonable, kindly verify the original candle dimensions, and we can calculate correctly from there.
But if the values stand, based on what was understood here, we find the height \( h \approx 0.00106 \) inches—definitely not aligning with typical height choices from your responses.
If you'd like a recalibration or re-evaluation of parameters, please share the correct figures!