Question

The length $\ell$, breadth b and thickness t of a block of wood were measured with the help of a measuring scale. The results with permissible errors are $\ell$ = 15.12 $\pm$ 0.01 cm, t = 5.28 $\pm$ 0.01 cm. $b$ = 10.15 $\pm$ 0.01 cm. The percentage error in volume upto proper significant figures is :

• A. 0.28%
• B. 0.36%
• C. 0.48%
• D. 0.64%

Answer 1

The correct option is B 0.36%

Volume, $V=lbt$

$\frac{dV}{V}=\frac{dl}{l}+\frac{db}{b}+\frac{dt}{t}$

The % error in volume,

$\frac{dV}{V}\times 100=(\frac{dl}{l}+\frac{db}{b}+\frac{dt}{t})\times 100=(\frac{0.01}{15.12}+\frac{0.01}{10.15}+\frac{0.01}{5.28})\times 100=0.36$%