Physics

# 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:

0.48%

##### SOLUTION

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

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

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

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

Now, the percentage error in volume

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

$\%\Delta V=0.48\%$

Hence, the percentage error in volume is 0.48.

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Single Correct Medium Published on 18th 08, 2020
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