Answer :
Based on the given statements and analysis, let's carefully review each student's statement to identify any mistakes.
1. Irma:
- Measured the radius using a ruler.
- Calculated the volume using an equation as [tex]\(104\ cm^3\)[/tex].
2. Julia:
- Measured the mass using a scale as [tex]\(0.6\ lb\)[/tex].
3. Grace:
- Used a scale to measure the weight as [tex]\(0.28\ lb\)[/tex].
4. Masha:
- Used a bucket of water and a ruler to measure the volume as [tex]\(98\ cm^3\)[/tex].
To identify the mistake, let's convert and check the consistency between the mass and weight measurements:
### Converting Mass and Weight:
- 1 lb is equivalent to 0.453592 kg.
- The weight is the mass multiplied by the acceleration due to gravity, which is approximately [tex]\(9.81\ m/s^2\)[/tex].
#### Calculating Julia's Mass in Kilograms:
- Julia’s mass = [tex]\(0.6\ lb\)[/tex]
- Julia’s mass in kg = [tex]\(0.6 \times 0.453592 \approx 0.2721552\ kg\)[/tex]
#### Converting Grace's Weight to Kilograms:
- Grace’s weight = [tex]\(0.28\ lb\)[/tex]
- Grace’s weight in kg = [tex]\(0.28 \times 0.453592 \approx 0.12700576\ kg\)[/tex]
### Checking Consistency:
- According to physics, weight (force) is mass times acceleration due to gravity ([tex]\(9.81\ m/s^2\)[/tex]).
#### Calculating Expected Weight from Julia's Mass:
- Expected weight (Newton) = [tex]\(0.2721552\ kg \times 9.81\ m/s^2 \approx 2.668853592\ N \)[/tex]
#### Converting Expected Weight Back to Pounds:
- Expected weight in pounds (lb) = [tex]\(2.668853592\ N \times 0.101972 \approx 0.2718999852\ lb\)[/tex]
### Evaluating the Statements:
Grace's measured weight (0.28 lb) significantly deviates from the expected weight based on Julia's mass and the principles of physics.
Given the information and detailed reasoning, the mistake is in Grace's measurement of the weight. Therefore:
Grace made a mistake in her statement.
1. Irma:
- Measured the radius using a ruler.
- Calculated the volume using an equation as [tex]\(104\ cm^3\)[/tex].
2. Julia:
- Measured the mass using a scale as [tex]\(0.6\ lb\)[/tex].
3. Grace:
- Used a scale to measure the weight as [tex]\(0.28\ lb\)[/tex].
4. Masha:
- Used a bucket of water and a ruler to measure the volume as [tex]\(98\ cm^3\)[/tex].
To identify the mistake, let's convert and check the consistency between the mass and weight measurements:
### Converting Mass and Weight:
- 1 lb is equivalent to 0.453592 kg.
- The weight is the mass multiplied by the acceleration due to gravity, which is approximately [tex]\(9.81\ m/s^2\)[/tex].
#### Calculating Julia's Mass in Kilograms:
- Julia’s mass = [tex]\(0.6\ lb\)[/tex]
- Julia’s mass in kg = [tex]\(0.6 \times 0.453592 \approx 0.2721552\ kg\)[/tex]
#### Converting Grace's Weight to Kilograms:
- Grace’s weight = [tex]\(0.28\ lb\)[/tex]
- Grace’s weight in kg = [tex]\(0.28 \times 0.453592 \approx 0.12700576\ kg\)[/tex]
### Checking Consistency:
- According to physics, weight (force) is mass times acceleration due to gravity ([tex]\(9.81\ m/s^2\)[/tex]).
#### Calculating Expected Weight from Julia's Mass:
- Expected weight (Newton) = [tex]\(0.2721552\ kg \times 9.81\ m/s^2 \approx 2.668853592\ N \)[/tex]
#### Converting Expected Weight Back to Pounds:
- Expected weight in pounds (lb) = [tex]\(2.668853592\ N \times 0.101972 \approx 0.2718999852\ lb\)[/tex]
### Evaluating the Statements:
Grace's measured weight (0.28 lb) significantly deviates from the expected weight based on Julia's mass and the principles of physics.
Given the information and detailed reasoning, the mistake is in Grace's measurement of the weight. Therefore:
Grace made a mistake in her statement.
