Question

The length, breadth and thickness of a block are measured with the help of a meter scale. given $\ell$ =(5.12 + 0.01)cm, b =(10.15 +0.01)cm, t=(5.28+0.01)cm. The percentage error in volume is:

• A. 0.64%
• B. 0.28%
• C. 0.37%
• D. 0.48%

Answer 1

The correct option is D 0.48%

Given that,

Length of the block $l=(5.12+0.01)$cm

Breadth of the block $b=(10.15+0.01)$ cm

Thickness of the block $t=(5.28+0.01)$ cm

We know that,

Relative error in volume of cuboid

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

$\frac{dV}{V}=\frac{0.01}{5.12}+\frac{0.01}{10.15}+\frac{0.01}{5.28}$

$\frac{dV}{V}=\frac{1}{512}+\frac{1}{1015}+\frac{1}{528}$

Now, the percentage error in volume

$\frac{\Delta V}{V}\times 100=0.48$

$\%\Delta V=0.48\%$

Hence, the percentage error in volume is 0.48.