Question

The dimensions of a rectangular block measured with callipers having least count of $0.01 cm$ are $5 mm \times 10 mm \times 5 mm$. 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
$\frac{\Delta V}{V} \times 100=\frac{\Delta L}{L} \times 100+\frac{\Delta B}{B} \times 100+\frac{\Delta H}{H} \times 100$
$=\frac{0.01}{0.5} \times 100+\frac{0.01}{1.0} \times 100+\frac{0.01}{0.5} \times 100$
$=2 \%+1 \%+2 \%=5 \%$