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

Explanation

Given that
`(dx)/x xx 100 = 1%`
Let volume of cube be V.
`:. V=x^(3)`
`rArr (dV0/(dx) = 3x^(2)`
` rArr (dV)/V = (3*x^(2)dx)/V = (3x^(2)dx)/x^(3) = 3 * (dx)/x`
` rArr (dV)/V xx 100 = 3 * (dx)/x xx 100`
` rArr" Percentage increase in volume " 3 xx 1% = 3%` .