Asked by Chris
Gas is escaping a round balloon at2units^2/min.How fast is the surface area shrinking when the radius is 12units?
Answers
Answered by
Damon
Volume = V = (4/3) pi r^3
area =A = 4 pi r^2
r = (A/4pi)^.5
so
V = (4/3) pi (A/4pi)^1.5
dV/dt = (4/3)(1/5)(A/4pi)^.5 (dA/dt/4pi)
here dV/dt = -2
r = 12 so A = 4 pi(144)
solve for dA/dt
area =A = 4 pi r^2
r = (A/4pi)^.5
so
V = (4/3) pi (A/4pi)^1.5
dV/dt = (4/3)(1/5)(A/4pi)^.5 (dA/dt/4pi)
here dV/dt = -2
r = 12 so A = 4 pi(144)
solve for dA/dt
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.