Question
Mia is calculating the volume of the cylinder below using the following work.
A cylinder with height of 47 meters and diameter of 35 meters.
mc018-2.jpg
What was Mia’s first error?
She confused the height and the diameter.
She forgot to include pi as a factor in the volume expression.
She applied the exponent before multiplying 17.5 and 47.
She squared 17.5 instead of 35.
A cylinder with height of 47 meters and diameter of 35 meters.
mc018-2.jpg
What was Mia’s first error?
She confused the height and the diameter.
She forgot to include pi as a factor in the volume expression.
She applied the exponent before multiplying 17.5 and 47.
She squared 17.5 instead of 35.
Answers
Answered by
GPT-4o mini
To find the volume of a cylinder, the formula is:
\[
V = \pi r^2 h
\]
Where \( r \) is the radius and \( h \) is the height of the cylinder.
Given:
- Height \( h = 47 \) meters
- Diameter = \( 35 \) meters
To find the radius \( r \), we use the formula:
\[
r = \frac{d}{2} = \frac{35}{2} = 17.5 \text{ meters}
\]
Now, we can identify Mia's first error based on the options provided:
1. **She confused the height and the diameter.** - This is not an error since she correctly identified the height as 47 meters and the diameter as 35 meters.
2. **She forgot to include pi as a factor in the volume expression.** - This could be a potential error if she calculated without using π, but it does not describe her initial mistake.
3. **She applied the exponent before multiplying 17.5 and 47.** - This statement does not directly address an initial error in the context of this problem.
4. **She squared 17.5 instead of 35.** - This option is not correct because squaring the radius (17.5) is the correct step in the formula.
Based on common mistakes, if she calculated using the radius incorrectly before the application of the formula, the most likely initial error would be that:
**She forgot to include pi as a factor in the volume expression.**
However, since the correct choice is somewhat unclear without more context on her calculations, it's important to understand that the right approach should have included π from the start. If she squared the diameter directly instead of the radius, that would have also constituted an error.
The most fitting answer from the choices provided, assuming a straightforward understanding, would be:
**She squared 17.5 instead of 35** - If that was understood in the context of calculating without recognizing the need to square the radius rather than the diameter directly.
\[
V = \pi r^2 h
\]
Where \( r \) is the radius and \( h \) is the height of the cylinder.
Given:
- Height \( h = 47 \) meters
- Diameter = \( 35 \) meters
To find the radius \( r \), we use the formula:
\[
r = \frac{d}{2} = \frac{35}{2} = 17.5 \text{ meters}
\]
Now, we can identify Mia's first error based on the options provided:
1. **She confused the height and the diameter.** - This is not an error since she correctly identified the height as 47 meters and the diameter as 35 meters.
2. **She forgot to include pi as a factor in the volume expression.** - This could be a potential error if she calculated without using π, but it does not describe her initial mistake.
3. **She applied the exponent before multiplying 17.5 and 47.** - This statement does not directly address an initial error in the context of this problem.
4. **She squared 17.5 instead of 35.** - This option is not correct because squaring the radius (17.5) is the correct step in the formula.
Based on common mistakes, if she calculated using the radius incorrectly before the application of the formula, the most likely initial error would be that:
**She forgot to include pi as a factor in the volume expression.**
However, since the correct choice is somewhat unclear without more context on her calculations, it's important to understand that the right approach should have included π from the start. If she squared the diameter directly instead of the radius, that would have also constituted an error.
The most fitting answer from the choices provided, assuming a straightforward understanding, would be:
**She squared 17.5 instead of 35** - If that was understood in the context of calculating without recognizing the need to square the radius rather than the diameter directly.