Given
- C(t) = 40 cm + t·(2/5 cm/s) . . . circumference of a circle vs time
Find
- dr/dt for radius r
- r at t=4 seconds
Solution
The circumference and radius of a circle are related by
... C = 2πr
so the radius in terms of circumference is
... r = C/(2π)
... r(t) = (40 +0.4t)/(2π) = (1/π)(20 cm + 0.2t cm/s)
Then dr/dt is
... dr/dt = 0.2/π cm/s
And the radius at t=4 s is
... r(4) = (1/π)(20 + 0.2·4) cm
... r(4) = 20.8/π cm
