Find the approximate change in the volume V of a cube of side x metres caused by increasing the side by 1%.

Explanation

Let `a` is the side of the cube.
Then, volume of the cube, `V = a^3`

Now, `(dV)/(da) = 3a^2`

`=>dV = 3a^2 *da`

It is given that `da = 1%` of `a= a/100`

`=>dV = 3a^2*a/100 = 3/100*a^3`

`=>dV = 3/100*V`

`=>dV = 3%` of `V = 0.03V`

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