Question

the side of a cube, as measured with a vernier calipers of least count $0.01cm$ is $3.00cm$.The maximum, possible error in the measurement of volume is

• A. $\pm 0.01c{m}^3$
• B. $\pm 0.06c{m}^3$
• C. $\pm 0.00c{m}^3$
• D. $\pm 0.27c{m}^3$

Answer 1

The correct option is D $\pm 0.27c{m}^3$

$\begin{array}{c}V=a^3\\ \text{differentiating both sides}\\ dv=3a^{2}da\end{array}$

$\begin{array}{c}=3\times 3^2\times 0.01\\ =3\times 9\times 0.01\\ =27\times 0.01\\ =0.275{cm}^3\end{array}$