Question

Length, breadth and thickness of a strip having a uniform cross section are measured to be $ 10.5 \, \text{cm}, 0.05 \, \text{mm} $, and $ 6.0 \, \mu\text{m} $, respectively. Which of the following option(s) give(s) the volume of the strip in $ \text{cm}^3 $ with correct significant figures:

• A. \( 3.2 \times 10^{-5} \)
• B. \( 32.0 \times 10^{-6} \)
• C. \( 3.0 \times 10^{-5} \)
• D. \( 3 \times 10^{-5} \)

Hint:

Always convert all measurements to the same unit system before calculating physical quantities like volume. Then, round the final answer to match the least number of significant figures from the inputs.

Answer 1

The Correct Option is D

1. Convert all measurements to cm:

• Length: 10.5 cm
• Breadth: 0.05 mm = 0.05 / 10 cm = 0.005 cm
• Thickness: 6.0 $\mu$m = 6.0 / $10^6$ m = 6.0 / $10^4$ cm = 0.0006 cm

2. Calculate the volume:

• Volume = Length Breadth Thickness
• Volume = 10.5 cm 0.005 cm 0.0006 cm = 3.15 $10^{-5}$ cm$^3$

3. Significant Figures:

• Length: 10.5 cm (3 significant figures)
• Breadth: 0.005 cm (1 significant figure)
• Thickness: 0.0006 cm (1 significant figure)
• When multiplying, the result should have the same number of significant figures as the measurement with the \textit{least} number of significant figures. In this case, that's 1.

4. Round the result:

• 3.15 $10^{-5}$ cm$^3$ rounded to 1 significant figure is 3 $10^{-5}$ cm$^3$

Therefore, the answer is (D) 3 x $10^{-5}$.