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VITEEE 2014 Paper

Section: Mathematics

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Question : 94 of 120

Marks: +1, -0

If there is an error of

k\%

in measuring the edge of a cube, then the percent error in estimating its volume is

k
3k
$\frac{k}{3}$
None of these

Solution:

Volume V of a cube of side x is given by

V = x^3

⇒

\frac{dv}{dx} = 3x^2

Let the change in x be

\Delta x = K\%

of

x = \frac{kx}{100}

Now, the change in volume,

\Delta V = \left(\frac{dV}{dx}\right) \Delta x = 3x^3 (\Delta x)

= 3x^2 \left(\frac{kx}{100}\right) = \frac{3x^3 \cdot k}{100}

∴ Approximate change in volume

= \frac{3k x^3}{100} = \frac{3k}{100} \cdot x^3

= 3K\%

of original volume

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