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:
Show Hint
- \( 3.2 \times 10^{-5} \)
- \( 32.0 \times 10^{-6} \)
- \( 3.0 \times 10^{-5} \)
\( 3 \times 10^{-5} \)
The Correct Option is D
Solution and Explanation
- 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
- Volume = Length Breadth Thickness
- Volume = 10.5 cm 0.005 cm 0.0006 cm = 3.15 $10^{-5}$ cm$^3$
- 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.
- 3.15 $10^{-5}$ cm$^3$ rounded to 1 significant figure is 3 $10^{-5}$ cm$^3$
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