Question

The percentage error in the measurement of side of a cube is 1%what will be the percentage error calculation of its volume

Answer 1

Answer:

Percentage error in volume = 3%

Explanation:

We know that, for a cube of side 'a' volume is given by

Volume = a³

Hence, on taking percentage error on both sides we get,

$\dfrac{\Delta V}{V} = 3\dfrac{\Delta a}{a}$

We are multiplying $\dfrac{\Delta a }{a}$ by 3 because it had the power 3

Given in the question that,

Percentage error in side = $\dfrac{\Delta a }{a}$  = 1%

Putting this value in we get,

$\dfrac{\Delta V}{V} = 3 \times 1 =$ 3%

Answer 2

Answer

Let the side of cube be a

Volume = ${a}^{3}$

Percentage error = n ( percentage error in value of a )

where n is the power of a

Percentage error in volume =

$\frac{\Delta v}{v} \times 100\% = 3 \frac{\Delta a}{a}$

$\frac{\Delta a}{a} = 1% ( given)$

$\frac{\Delta v}{v} \times 100\% = 3 \times 1\% = 3\%$

ADDITIONAL INFORMATION :-

Let n be number of values for a physical quantity which is$a_1 , a_2 , a_3 - - - a_n$

Average value = $\frac{a_1 + a_2 + a_3 - - - a_n}{n}$

Absolute error = Difference between true value and measured value.

Thanks