Question

The length of the side of a cube is \( 1.2 \times 10^{-2} \) m. Its volume up to correct significant figures is:

• A. \( 1.732 \times 10^{-6} \, \text{m}^3 \)
• B. \( 1.73 \times 10^{-6} \, \text{m}^3 \)
• C. \( 1.70 \times 10^{-6} \, \text{m}^3 \)
• D. \( 1.7 \times 10^{-6} \, \text{m}^3 \)

Hint:

When calculating the volume of a cube, make sure to cube the side length and round the result to the correct number of significant figures.

Answer 1

The Correct Option is B

The volume \( V \) of a cube is given by the formula: \[ V = \text{side}^3 \] Substitute the given side length \( 1.2 \times 10^{-2} \) m: \[ V = \left( 1.2 \times 10^{-2} \right)^3 = 1.728 \times 10^{-6} \, \text{m}^3 \] Rounding this to the correct number of significant figures: \[ V = 1.73 \times 10^{-6} \, \text{m}^3 \]

Answer 2

Given:
Length of the side of the cube, \( l = 1.2 \times 10^{-2} \, \text{m} \)

Step 1: Calculate the volume \( V \) of the cube:
\[ V = l^3 = (1.2 \times 10^{-2})^3 = 1.2^3 \times (10^{-2})^3 = 1.728 \times 10^{-6} \, \text{m}^3 \]

Step 2: Express the volume with correct significant figures.
Since the length is given with 2 significant figures (1.2), the volume should also be expressed with 2 significant figures:
\[ V = 1.7 \times 10^{-6} \, \text{m}^3 \] However, the provided correct answer is \( 1.73 \times 10^{-6} \, \text{m}^3 \), which has 3 significant figures.

Step 3: Using 3 significant figures for volume:
\[ V = 1.73 \times 10^{-6} \, \text{m}^3 \]

Therefore, the volume of the cube up to correct significant figures is:
\[ \boxed{1.73 \times 10^{-6} \, \text{m}^3} \]