Volume Calculation of Strip with Significant Figures

To find the volume of the strip with the correct number of significant figures, we follow the rules of significant figures for multiplication.

Step 1: Convert all given quantities to centimeters ($\text{cm}$)

• Length ($l$): $l = 10.5\text{ cm}$
• Breadth ($b$): $b = 0.05\text{ mm} = 0.005\text{ cm} = 5 \times 10^{-3}\text{ cm}$
• Thickness ($t$): $t = 6.0\text{ }\mu\text{m} = 6.0 \times 10^{-4}\text{ cm}$

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Step 2: Determine the number of significant figures for each measurement

• $l = 10.5\text{ cm} \rightarrow 3 \text{ significant figures}$
• $b = 0.05\text{ mm} \rightarrow 1 \text{ significant figure (leading zeros are not significant)}$
• $t = 6.0\text{ }\mu\text{m} \rightarrow 2 \text{ significant figures}$

The rule for multiplication states that the final result must be reported with the same number of significant figures as the measurement with the least number of significant figures. Here, the minimum number of significant figures is $1$ (from the breadth $b$).

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Step 3: Calculate the volume

The volume $V$ of the rectangular strip is given by: $V = l \times b \times t$

Substituting the values: $V = 10.5\text{ cm} \times (0.005\text{ cm}) \times (6.0 \times 10^{-4}\text{ cm})$ $V = 3.15 \times 10^{-5}\text{ cm}^3$

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Step 4: Round off to the correct number of significant figures

Rounding $3.15 \times 10^{-5}\text{ cm}^3$ to $1$ significant figure: $V \approx 3 \times 10^{-5}\text{ cm}^3$

Thus, the correct option is (D).