A spherically shaped balloon is being inflated so that the radius is changing at a constant rate of 2 in./sec. Find an algebraic representation for V(t), the volume in terms of time, t.
Would this be the right algebraic equation, ?
Adding r inside the parentheses is redundant because r=2t. You see what I mean? So everything is right, but I would write the eqaution like this:
V(t)=(4/3)(pi)(2t)^3
Does that help you at all?
I doubt that the problem requires previous Knowlege of the original radius. I mean, It's a balloon. It could be laying down flat before it was inflated, or possibly wrinkled. Yeah, maybe, but if I was your teacher, the answer I gave you is the one I would be looking for.