Question

The dimensions of a rectangular block measured with callipers having least count of $0.01cm$ are $5mm\times 10mm\times 5mm$. The maximum percentage error in the measurement of the volume of the block is

• A. $5\%$
• B. $10\%$
• C. $15\%$
• D. $20\%$

Answer 1

Answer: (A)

Volume $=$ Length $\times$ Breadth $\times$ Height
$V=L\times B\times H$
The maximum relative error in $V$ is
$\frac{\Delta V}{V}=\frac{\Delta L}{L}+\frac{\Delta B}{B}+\frac{\Delta H}{H}$
The maximum percentage error in $V$ is
$\frac{\Delta V}{V}\times 100=\frac{\Delta L}{L}\times 100+\frac{\Delta B}{B}\times 100+\frac{\Delta H}{H}\times 100$
$=\frac{0.01}{0.5}\times 100+\frac{0.01}{1.0}\times 100+\frac{0.01}{0.5}\times 100$
$=2\%+1\%+2\%=5\%$