Question

There is an error of 2% in the measurement of side of a cube the percentage error in calculation of volume will be

Answer 1

answer- 2percent (OK friends)

Answer 2

The percentage error in volume is 6%

GIVEN

Percentage error of side of cube- 2%

TO FIND:

Percentage error in volume.

SOLUTION:

We can simply solve the above problem as under -

Let, Side of cube = a

it is given that,

the percentage error in measuring side of cube = 2%

or,

$\frac{∆a}{a} \times 100 = 2\%$

we know that,

$volume \: of \: cube = {a}^{3}$

expanding it in the language of error -

$\frac{∆v}{v} = 3 \times \frac{∆a}{a}$

Multiplying the above equation with 100 to find the percentage error-

$\frac{∆v}{v} \times 100 = 3 \times \frac{∆a}{a} \times 100$

putting the value of ∆a/a×100, we get

$\frac{∆v}{v} \times 100 = 3 \times 2$

$\frac{∆v}{v} \times 100 = 6$

Percentage Error In Volume = 6%

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