Asked by Brian
The area of a circle is increasing at a rate of 12pi ft^2/sec. At what rate is the radius of 6ft. increasing?
Answers
Answered by
oobleck
The engineer's way.
As the radius grows by dr, the area grows by the circumference times dr. That is
dA = C*dr = 2πr dr
so, when dA=12 and r=6, dr=1
Or, as they want you to use calculus,
A = πr^2
dA/dt = 2πr dr/dt
12π = 2π*6 * dr/dt
dr/dt = 1 ft/s
As the radius grows by dr, the area grows by the circumference times dr. That is
dA = C*dr = 2πr dr
so, when dA=12 and r=6, dr=1
Or, as they want you to use calculus,
A = πr^2
dA/dt = 2πr dr/dt
12π = 2π*6 * dr/dt
dr/dt = 1 ft/s
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.