**Solution:**

**Hint:** When calculating the area and volume, it's important to consider the given significant figures for each measurement. Results should be rounded to the least significant figures among the given measurements.

**Complete step by step solution:**

1. Given Values:

Length of sheet, l = 4.234m

Breadth of sheet, b = 1.005m

Thickness of sheet, h = 2.01cm = 0.0201m

The Provided Table Lists the Significant Figures:

Quantity | Number | Significant Figure |

I | 4.234 | 4 |

b | 1.005 | 4 |

h | 0.0201 | 3 |

2. Calculating the Surface Area:

The surface area of the sheet is the sum of the areas of its six sides:

Area $= 2(l \times b + b \times h + h \times l)$

Area $= 2(4.234\text{m} \times 1.005\text{m} + 1.005\text{m} \times 0.0201\text{m} + 4.234\text{m} \times 0.0201\text{m})$

Area $= 2(4.25517\text{m}^2 + 0.0202005\text{m}^2 + 0.0851154\text{m}^2)$

Area $= 2 \times 4.3604854\text{m}^2$

Area $= 8.7209708\text{m}^2$

Rounding to 3 significant figures (smallest number of significant figures provided), we get:

Area $\approx 8.72\text{m}^2$

3. Calculating the Volume:

Volume of the rectangular sheet is given by:

Volume $= l \times b \times h $

Volume $= 4.234\text{m} \times 1.005\text{m} \times 0.0201\text{m} $

Volume $= 0.085324134\text{m}^3$

Rounding to 3 significant figures, we get:

Volume $\approx 0.0853\text{m}^3$

**Note:** When dealing with significant figures, always ensure that the final answer is rounded off to the least number of significant figures among the measurements used. In this case, the thickness had the smallest number of significant figures (3), so our answers for both area and volume were rounded off to 3 significant figures.