Find the approximate percentage increase in a cube of side x metre if the percentage increase in its side is 1%.

Explanation

Given that
`(dx)/x xx 100 = 1%`
Let volume of cube -V
`:. V=x^(3)`
` rArr (dV)/(dx) = 3x^(3)`
` 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%`.