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

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} $

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