You also measure the length of a side of the cube using a ruler and get the value 3.15+0.05 cm. Calculate the volume of the cube and the uncertainty the calculated value and report it in the format V±õV, rounded appropriately. The volume of a cube is V=L³. (1m L = 1 cm3) cm3
You also measure the length of a side of the cube using a ruler and get the value 3.15+0.05 cm. Calculate the volume of the cube and the uncertainty the calculated value and report it in the format V±õV, rounded appropriately. The volume of a cube is V=L³. (1m L = 1 cm3) cm3
College Physics
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ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![### Calculating the Volume and Uncertainty of a Cube
To determine the volume of a cube, you measure the length of a side using a ruler. You obtained a length of 3.15 ± 0.05 cm. The task is to calculate the volume of the cube and the uncertainty in the calculated value, and then report it in the specified format: \( V \pm \delta V \), rounded appropriately.
The formula for the volume of a cube is:
\[ V = L^3 \]
where:
- \( L \) is the length of a side of the cube.
- Given \( L = 3.15 \pm 0.05 \) cm.
1. Calculate the nominal volume:
\[ V = (3.15 \, \text{cm})^3 = 31.314375 \, \text{cm}^3 \]
After rounding, this becomes:
\[ V \approx 31.31\, \text{cm}^3 \]
2. Calculate the uncertainty in the volume, \( \delta V \):
\[ \delta V = |3(L \pm \delta L)^2 \cdot \delta L| \]
\[ \delta V = |3 \times (3.15 \, \text{cm})^2 \times 0.05 \, \text{cm}| \]
\[ \delta V = |3 \times 9.9225 \, \text{cm}^2 \times 0.05 \, \text{cm}| \]
\[ \delta V \approx 1.49 \, \text{cm}^3 \]
Now, expressing the calculated volume with its uncertainty in the format \( V \pm \delta V \), we get:
\[ V \pm \delta V = 31.31 \pm 1.49 \, \text{cm}^3 \]
### Interactive Problem Reporting
For recording your results:
- Enter the nominal volume in the first box.
- Enter the uncertainty in the second box.
\[ [ \text{31.31} ] \pm [ \text{1.49} ] \, \text{cm}^3 \]
Feel free to use this example as a guide in solving similar problems involving measurements and uncertainty calculations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff5bd1a27-e559-4abd-b158-898799f60d66%2Fa9842c88-5b52-49eb-8e17-5b3e4fad2f25%2Ff7vzk6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Calculating the Volume and Uncertainty of a Cube
To determine the volume of a cube, you measure the length of a side using a ruler. You obtained a length of 3.15 ± 0.05 cm. The task is to calculate the volume of the cube and the uncertainty in the calculated value, and then report it in the specified format: \( V \pm \delta V \), rounded appropriately.
The formula for the volume of a cube is:
\[ V = L^3 \]
where:
- \( L \) is the length of a side of the cube.
- Given \( L = 3.15 \pm 0.05 \) cm.
1. Calculate the nominal volume:
\[ V = (3.15 \, \text{cm})^3 = 31.314375 \, \text{cm}^3 \]
After rounding, this becomes:
\[ V \approx 31.31\, \text{cm}^3 \]
2. Calculate the uncertainty in the volume, \( \delta V \):
\[ \delta V = |3(L \pm \delta L)^2 \cdot \delta L| \]
\[ \delta V = |3 \times (3.15 \, \text{cm})^2 \times 0.05 \, \text{cm}| \]
\[ \delta V = |3 \times 9.9225 \, \text{cm}^2 \times 0.05 \, \text{cm}| \]
\[ \delta V \approx 1.49 \, \text{cm}^3 \]
Now, expressing the calculated volume with its uncertainty in the format \( V \pm \delta V \), we get:
\[ V \pm \delta V = 31.31 \pm 1.49 \, \text{cm}^3 \]
### Interactive Problem Reporting
For recording your results:
- Enter the nominal volume in the first box.
- Enter the uncertainty in the second box.
\[ [ \text{31.31} ] \pm [ \text{1.49} ] \, \text{cm}^3 \]
Feel free to use this example as a guide in solving similar problems involving measurements and uncertainty calculations.
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What is the percent error in the accuracy in the measured volume of the cube? Use the calculated value as the expected value. Round your answer to 2 digits.
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