Question

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

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

Answer 1

The correct option is A 5 %

Length $L=10mm$

Breadth $B=5mm$

Height $H=5mm$

Error in length, breadth and height $\Delta L=\Delta B=\Delta H=0.1mm$

Volume of block $V=L\times B\times H$

Percentage error in volume $\frac{\Delta V}{V}\times 100=(\frac{\Delta L}{L}\times 100)+(\frac{\Delta B}{B}\times 100)+(\frac{\Delta H}{H}\times 100)$

$⟹$ $\frac{\Delta V}{V}\times 100=(\frac{0.1}{10}\times 100)+(\frac{0.1}{5}\times 100)+(\frac{0.1}{5}\times 100)=5$ %