A spherical balloon is inflated so that its radius increases at 2 cm per second. At the instant its radius is 3 cm, how fast is its volume increasing?
Correct answer: C. 36π cm³/s
- A. 18π cm³/s
- B. 24π cm³/s
- C. 36π cm³/s
- D. 54π cm³/s
Explanation
The volume is V = (4/3)πr³, so dV/dt = 4πr² dr/dt. Substituting r = 3 and dr/dt = 2 gives 4π(9)(2) = 72π cm³/s, so none of the listed options is correct. The options should include 72π cm³/s.
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