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  • The length and breadth of a rectangular sheet are 16.2 \; cm and 10.1 \; cm respectively. The area of the sheet in appropriate significant figures and error is: a) 164\pm 3\; cm^{2} b) 163.62\pm 2.6\; cm^{2} c) 163.6\pm 2.6\; cm^{2}

The length and breadth of a rectangular sheet are 16.2 \; cm and 10.1 \; cm respectively. The area of the sheet in appropriate significant figures and error is:

a) 164\pm 3\; cm^{2}

b) 163.62\pm 2.6\; cm^{2}

c) 163.6\pm 2.6\; cm^{2}

d) 163.62\pm 3\; cm^{2}

Answers (1)

The answer is option (i) 164\pm 3\; cm^{2}

Explanation: Given :

l=16.2\; cm,\; and \; \Delta l=0.1

b=10.1\; cm,\; \Delta b=0.1

l=16.1\pm 0.1\; and\; b=10.1\pm 0.1

Now,  area (a) =l\times b

                       =16.2\times 10.1

                       =163.62\; cm^{2}

                      =164\; cm^{2}

(by rounding off the answer of the area in 3 significant numbers)

\Delta \frac{A}{A}=\frac{\Delta l}{l}+\frac{\Delta b}{b}

=\frac{0.1}{16.2}+\frac{0.1}{10.1}

\frac{\Delta A}{164}=(\frac{10.1\times0.1+16.2\times0.1}{16.2\times10.1})

Thus, \Delta A=2.64\; cm^{2}

We get \Delta A= 3\; cm^{2}

(by rounding off the answer of  \Delta A in 1 significant number)

Thus, \Delta A=(164\pm 3)cm^{2}          

Posted by

infoexpert22

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