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Question

The length $l$ breadth b and Thickness t of a block of steel are measured with the help of a measuring scale. The results (in cm) are $l = 10 \pm 0.01, b = 5 \pm 0.01 a n d t = 3 \pm 0.01$ . Then maximum possible error in the volume is

Moderate

Solution

$V = l b t$
$∴ \frac{∆ V}{V} = \frac{∆ l}{l} + \frac{∆ b}{b} + \frac{∆ t}{t} = \frac{0.01}{10} + \frac{0.01}{5} + \frac{0.01}{3}$
$∴ \frac{∆ V}{V} x 100 % = 0.1 % + 0.2 % + 0.33 % = 0.63 %$

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