# (solved)Question 2.11 of NCERT Class XI Physics Chapter 2

The length, breadth and thickness of a rectangular sheet of metal are 4.234 m, 1.005 m, and 2.01 cm respectively. Give the area and volume of the sheet to correct significant figures.

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### Question 2.11 NCERT Class XI Physics

The length, breadth and thickness of a rectangular sheet of metal are 4.234 m, 1.005 m, and 2.01 cm respectively. Give the area and volume of the sheet to correct significant figures.

### Physical Concept

Formula for area will be the total surface area of a cuboid - 2x(lb + bh + hl), where l = length, b = breadth and h= thickness. And volume will be length x breadth x thickness.

Significant figures in the given measurements are 4.234 [4], 1.005[4] and 2.01[3]. The least S.F. are in 2.01, i.e., three.

First we make algeabraic calculation, then round off the result to three significant figures.

### Solution

$\displaystyle l = 4.234 \text{ m}, b = 1.005 \text{ m}, h = 2.01 \text{ cm}$

$\displaystyle \text{S.F. are } l (4), b (4), h (3)$

$\displaystyle \text{S.F. in answer will be min(4, 4, 3) i.e., 3}$

$\displaystyle \text{convert } h \text{ to meters, } \therefore h = 0.0201\text{m}$

\begin{aligned} &\text{Total surface area}\\ &= 2 \times (lb + bh + hl)\\ &=2 \times( 4.234 \cdot 1.005 + 1.005 \cdot 0.0201 + 0.0201 \cdot 4.234)\\ &= 2 \times(4.25517 + 0.0202005 + 0.0851034)\\ &= 8.7209478\\ &\therefore \text{rounding to 3 we get } 8.72 \text{ m}^2\:\underline{Ans} \end{aligned}