$c\frac{m}{m}inr=50$ centimeters and $r=75$ centimeters.

$r.=50$

$c\frac{m}{m}in$

$r=75$

$c\frac{m}{m}in$

$(b)$ Explain why the rate $of$ change $of$ the radius $of$ the sphere $is$ not

constant even though $\frac{dV}{dt}is$ constant.

The rate $of$ change $of$ the radius $is$ a linear relationship whose

slope $is\frac{dV}{dt}.$

$\frac{dr}{dt}as$ a function runs parallel $to$ the volume function, which $is$

not linear.

The volume only appears constant; $itis$ actually a rational

relationship.

$If\frac{dr}{dt}is$ constant, $\frac{dV}{dt}$ depends $on{r}^2.$

The rate $of$ change $of$ the radius $is$ a cubic relationship.