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:

Step 1: Identify the given measurements.

The dimensions of the strip are:

$$L = 10.5\text{ cm}$$ $$b = 0.05\text{ mm}$$ $$t = 6.0\ \mu\text{m}$$

Step 2: Convert all dimensions to centimeters.

Convert breadth and thickness to centimeters.

$$b = 0.005\text{ cm}$$ $$t = 6.0 \times 10^{-4}\text{ cm}$$

Step 3: Calculate the volume.

Use the formula for the volume of a rectangular strip.

$$V = L \cdot b \cdot t$$ $$V = 10.5 \times 0.005 \times 6.0 \times 10^{-4}$$ $$V = 3.15 \times 10^{-5}\text{ cm}^{3}$$

Step 4: Determine the significant figures of each measurement.

Count the significant figures for each dimension.

• $10.5\text{ cm}$ has $3$ significant figures.
• $6.0\ \mu\text{m}$ has $2$ significant figures.
• $0.05\text{ mm}$ has $1$ significant figure.

Step 5: Round the final volume to the correct significant figures.

Since the least number of significant figures in the measurements is $1$, the result must be rounded to $1$ significant figure.

$$V = 3 \times 10^{-5}\text{ cm}^{3}$$

Answer: Option (4) $3 \times 10^{-5}\text{ cm}^{3}$ is correct.