Question

A balloon in the shape of a sphere is deflating. Given that t represents the time, in minutes, since it began losing air, the radius of the ballon (in cem) is r(t)=16-t. Let the equation V(r)= 4/3 pi r^3 represent the volume of a sphere of radius r. Find (V (open dot) r)(t)

Answer 1

V[open dot]r(t) (read V of r) is a shorthand for V(r(t)). The symbol [open dot] is a composition operator.

So
V[open dot]r(t)
=V(r(t))
=V(16-t)
=4/3 pi (16-t)^3

Simplify to complete the problem.

Answer 2

288