Question

Length, breadth and thickness of a block is measured using vernier calipers. The percentage errors in the measurements are 2%, 1% and 3% respectively. Estimate percentage error in the volume.

Answer 1

We know the volume of a block of length $\sf{l,}$ breadth $\sf{b}$ and thickness $\sf{h}$ is,

$\sf{\longrightarrow V=lbh}$

Then percentage error in the volume is given by,

$\sf{\longrightarrow \delta V=\delta l+\delta b+\delta h}$

where $\sf{\delta l,\ \delta b}$ and $\sf{\delta h}$ are percentage errors in length, breadth and height respectively.

In this question,

• $\sf{\delta l=2\%}$

• $\sf{\delta b=1\%}$

• $\sf{\delta h=3\%}$

Then,

$\sf{\longrightarrow \delta V=\delta l+\delta b+\delta h}$

$\sf{\longrightarrow \delta V=2\%+1\%+3\%}$

$\sf{\longrightarrow\underline{\underline{\delta V=6\%}}}$

Hence the percentage error in volume is 6%.