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 the option (i) 164\pm 3\; cm^{2}

Explanation: Given :

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

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

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

Now,  area (a) =I\times b

                       =16.2\times 10.1

                       =163.62\; cm^{2}

                      =164\; cm^{2}

\Delta \frac{A}{A}=\frac{\Delta I}{I}+\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=2.63\; cm^{2}

We get \Delta A= 3\; cm^{2} by rounding off \Delta I\; and\; \Delta b

Thus, \Delta A=(163\pm 3)cm^{2}          

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