NCERT Solutions

We need to calculate the total surface area and volume of a metal sheet using significant figure rules.

Concept: Surface area

The surface area $A$ and volume $V$ of a rectangular sheet are calculated using the dimensions of a rectangular parallelepiped. According to the rules of significant figures, the final result of a multiplication or division must have the same number of significant figures as the measurement with the least number of significant figures.

$$A = 2(lb + bt + tl)$$ $$V = l \times b \times t$$

Given:

• Length $l = 4.234\,\text{m}$ (4 significant figures)
• Breadth $b = 1.005\,\text{m}$ (4 significant figures)
• Thickness $t = 2.01\,\text{cm} = 0.0201\,\text{m}$ (3 significant figures)

Solving:

1. Calculate the total surface area:

$$\begin{aligned} A &= 2(4.234\,\text{m} \times 1.005\,\text{m} + 1.005\,\text{m} \times 0.0201\,\text{m} + 0.0201\,\text{m} \times 4.234\,\text{m}) \\ &= 2(4.25517\,\text{m}^2 + 0.0202005\,\text{m}^2 + 0.0851034\,\text{m}^2) \\ &= 2(4.3604739\,\text{m}^2) \\ &= 8.7209478\,\text{m}^2 \end{aligned}$$

Since the thickness $t$ has the least number of significant figures (3), we round the final area to 3 significant figures.

$$A \approx 8.72\,\text{m}^2$$

2. Calculate the volume:

$$\begin{aligned} V &= l \times b \times t \\ &= 4.234\,\text{m} \times 1.005\,\text{m} \times 0.0201\,\text{m} \\ &= 0.085528917\,\text{m}^3 \end{aligned}$$

Rounding to 3 significant figures (consistent with the thickness $t$):

$$V \approx 0.0855\,\text{m}^3$$

Answer

$$\text{Area} = 8.72\,\text{m}^2, \quad \text{Volume} = 0.0855\,\text{m}^3$$