Question

If the length & breadth of a rectangular surface are 32.2+or-0.2 cm & 12.5+or- 0.1 cm res. Calculate the % error in the measurement of surface area.

Answer 1

ΔA/A = [ΔL/L + Δb/b]

ΔA/A * 100 = (0.2/32.2 + 0.1/12.5) *100

ΔA/A * 100 = 1.42%

Answer 2

Answer:

The percentage error in the measurement of surface area is 1.42%.

Explanation:

Given the length of a rectangular surface,  $l= (32.2\pm0.2) cm$

The breadth of the rectangular surface, $b=(12.5\pm 0.1 )cm$

Area of the rectangular surface is given by the product of its length and breadth. i.e.,  $A=l\times b$

The error in the measurement is given by the ratio of absolute error to the measured value.

Thus, the percentage error is given by

$\%\mbox{error}=\dfrac{\mbox{absolute error}}{\mbox{measured value}}\times 100$

The percentage error in the area of the rectangular surface is given by

$\dfrac{\Delta A}{A}\times 100 =\dfrac{\Delta l}{l} \times 100+\dfrac{\Delta b}{b}\times 100$

                $=\dfrac{0.2}{32.2} \times 100+\dfrac{0.2}{12.5}\times 100$

                $=\dfrac{20}{32.2}+\dfrac{10}{12.5}=0.62+0.8=1.42$

Therefore, the percentage error in the measurement of surface area is 1.42%.

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