The dimensions of a rectangular block measured with a vernier callipers having least count of 0.1 mm is 5mm×10mm×5mm. The maximum percentage error in measurement of volume of the block is

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The dimensions of a rectangular block measured with a vernier callipers having least count of $0.1 m m$ is $5 m m \times 10 m m \times 5 m m .$ The maximum percentage error in measurement of volume of the block is

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Detailed Solution

V=xyz

Where x,y and z are the three dimensions then $\begin{array}{l} (\frac{Δ V}{V}) = (\frac{Δ x}{x} + \frac{Δ y}{y} + \frac{Δ z}{z}) \\ o r (\frac{Δ V}{V}) X 100 = (\frac{Δ x}{x} + \frac{Δ y}{y} + \frac{Δ z}{z}) × 100 \\ = (\frac{0.1}{5} + \frac{0.1}{10} + \frac{0.1}{5}) × 100 \\ = 5 % \end{array}$