Application of Derivatives · Class 12 · CBSE · Science Mathematics
The radius of a circular balloon is increasing at the rate of 0.5 cm/s. At what rate is its area increasing when the radius is 4 cm?
Practice question from Application of Derivatives (Class 12 · CBSE · Science Mathematics), with the correct answer and a step-by-step solution.
medium · MCQ · Q-C610AB
The radius of a circular balloon is increasing at the rate of 0.5 cm/s. At what rate is its area increasing when the radius is 4 cm?
- A.2π cm²/s
- B.4π cm²/sCorrect answer
- C.8π cm²/s
- D.16π cm²/s
Solution
For area A = πr², differentiating with respect to time gives dA/dt = 2πr·dr/dt. Substituting r = 4 cm and dr/dt = 0.5 cm/s gives dA/dt = 4π cm²/s.
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