The radius r, in inches, of a spherical balloon is related to the volume V by r(V)= ∛3V/4π

Question

Air is pumped into the balloon so the volume after t seconds is given by V(t)=16+14t.

a. Find the expression for the composite function r(V(t)).

b. What is the exact time in seconds when the radius reaches 12 inches?

For part a I got r(V(t)) = ∛(3(16+14t)/4π)

For part b is got 515.9 s and it says it's wrong. I've tried it a few times and keep getting a similar answer. What am I doing wrong?
Thanks

Answer 1

I used V = (4/3)π r^3 , with r = 12 to get
V = 7238.229...
then
7238.229 = 16 +14t
t = 515.8735...
Just like your answer.

using your r(V(t)) = ∛(3(16+14t)/4π)
12 = ∛(3(16+14t)/4π)
cube both sides
1728 = 3(16+14t)/(4π)
21714.68842 = 3(16+14t)
7238.229.. = 16+14t
7222.229.. = 14t
t = 515.8735... same thing.

mmmhhh?

Answer 2

Yeah, it's strange. Maybe the website is just glitching.
I appreciate the help regardless.
Thank you!!!

Answer 3

the exact time is 8/7 (144π - 1)