Answer
(a) $f(t)=t$
(b) $g(r) = \frac{4}{3}\pi r^3$
(c) $g∘f=\frac{4}{3}\pi t^3$
It represents the volume of the balloon for given $t$ seconds.
Work Step by Step
(a) According to the given information the radius increases by $1cm$ every $1sec$, so we can simply write a function:
$f(t)=t$
$t$ stands for time in $second$ and $f(t)$ radius of the sphere in $centimeter$.
(b) In general we have a formula of a volume, which is $=\frac{4}{3}\pi r^3$, so we can write:
$g(r) = \frac{4}{3}\pi r^3$
Where $r$ is radius in $centimeter$ and $g(r)$ volume in $centimeter^3$
(c) $g∘f=g(f(t))=g(t)= \frac{4}{3}\pi t^3$
$g∘f=\frac{4}{3}\pi t^3$
It represents the volume of the balloon for given $t$ seconds.
