alleryA spherical balloon's volume increases at 30 cm³/s. At r = 5 cm, how fast is the radius increasing?
A1 cm/s
B3/10π cm/s ≈ 0.095 cm/s
C30 cm/s
D2 cm/s
Answer & Solution
Correct answer: B. 3/10π cm/s ≈ 0.095 cm/s
V = (4/3)πr³. dV/dt = 4πr² dr/dt.
We have **So dr/dt = (dV/dt)/(4πr²).
That is **So dr/dt = 30/(4π × 25).
That is **So dr/dt = 30/(100π).
So **So dr/dt = 3/(10π) ≈ 0.0955 cm/s.**.
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