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If the length of a side of a cube is measured as 2.5 cm with an uncertainty of 0

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Question: If the length of a side of a cube is measured as 2.5 cm with an uncertainty of 0.1 cm, what is the volume of the cube with its uncertainty?

Options:

  1. 15.625 ± 0.25 cm³
  2. 15.625 ± 0.5 cm³
  3. 12.5 ± 0.1 cm³
  4. 10.0 ± 0.2 cm³

Correct Answer: 15.625 ± 0.25 cm³

Solution: 

Volume = (2.5 cm)³ = 15.625 cm³. The uncertainty in volume can be calculated using the formula for propagation of uncertainty.

If the length of a side of a cube is measured as 2.5 cm with an uncertainty of 0

Practice Questions

Q1
If the length of a side of a cube is measured as 2.5 cm with an uncertainty of 0.1 cm, what is the volume of the cube with its uncertainty?
  1. 15.625 ± 0.25 cm³
  2. 15.625 ± 0.5 cm³
  3. 12.5 ± 0.1 cm³
  4. 10.0 ± 0.2 cm³

Questions & Step-by-Step Solutions

If the length of a side of a cube is measured as 2.5 cm with an uncertainty of 0.1 cm, what is the volume of the cube with its uncertainty?
  • Step 1: Understand that the volume of a cube is calculated using the formula Volume = side length³.
  • Step 2: Identify the side length of the cube, which is given as 2.5 cm.
  • Step 3: Calculate the volume of the cube by cubing the side length: Volume = (2.5 cm)³.
  • Step 4: Perform the calculation: 2.5 × 2.5 = 6.25, and then 6.25 × 2.5 = 15.625 cm³.
  • Step 5: Now, we need to calculate the uncertainty in the volume. The formula for uncertainty in volume is: ΔV = 3 × (side length)² × ΔL, where ΔL is the uncertainty in the side length.
  • Step 6: Identify the uncertainty in the side length, which is given as 0.1 cm.
  • Step 7: Calculate the uncertainty in volume: ΔV = 3 × (2.5 cm)² × 0.1 cm.
  • Step 8: First, calculate (2.5 cm)² = 6.25 cm².
  • Step 9: Now, multiply: ΔV = 3 × 6.25 cm² × 0.1 cm = 1.875 cm³.
  • Step 10: Combine the volume and its uncertainty: The volume of the cube is 15.625 cm³ with an uncertainty of ±1.875 cm³.
  • Volume of a Cube – Understanding how to calculate the volume of a cube using the formula V = side³.
  • Uncertainty Propagation – Applying the rules of uncertainty propagation to calculate the uncertainty in derived quantities.
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