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?

Options:

Correct Answer: 16.0 cm³

Solution:

Volume = side³ = (2.5 cm)³ = 15.625 cm³. Considering significant figures, it is reported as 16.0 cm³.

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?

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?

Step 1: Understand that a cube has all sides of equal length.
Step 2: Identify the length of one side of the cube, which is given as 2.5 cm.
Step 3: Recognize that the formula for the volume of a cube is Volume = side × side × side (or side³).
Step 4: Calculate the volume using the formula: Volume = (2.5 cm) × (2.5 cm) × (2.5 cm).
Step 5: Perform the multiplication: (2.5 cm) × (2.5 cm) = 6.25 cm², then multiply by 2.5 cm again: 6.25 cm² × 2.5 cm = 15.625 cm³.
Step 6: Consider the uncertainty of 0.1 cm. Since the side length has 3 significant figures, the volume should be reported with 3 significant figures as well.
Step 7: Round 15.625 cm³ to 16.0 cm³ to reflect the correct number of significant figures.

Volume Calculation – Understanding how to calculate the volume of a cube using the formula V = side³.
Significant Figures – Applying the rules of significant figures to report the final answer correctly based on the precision of the measurements.
Uncertainty in Measurements – Recognizing how uncertainty in the measurement of the side length affects the final volume calculation.