#### Answer

change in volume percent: $\frac{dV}{V}=40%$

#### Work Step by Step

We are given:
$V=kr^4$
relative change for the function is shown by the relation: $\frac{dV}{V}$
$\frac{dV}{V}=\frac{4kr^3dr}{kr^4}$
$\frac{dV}{V}=\frac{4dr}{r}$
it is given that the increase in the value of r is 10%:
so $dr=0.1r$
$\frac{dV}{V}=\frac{4\times0.1r}{r}=0.4$
$\frac{dV}{V}=0.4\times100=40%$
$\frac{dV}{V}=40%$