Class 12

Math

Calculus

Application of Derivatives

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

Now, $dadV =3a_{2}$

$⇒dV=3a_{2}⋅da$

It is given that $da=1%$ of $a=100a $

$⇒dV=3a_{2}⋅100a =1003 ⋅a_{3}$

$⇒dV=1003 ⋅V$

$⇒dV=3%$ of $V=0.03V$

So, approximate change in the volume of the cube will be $0.03V$ and percentage change will be $3%$.