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If radius of circle is increasing at rate 0.5 cm/sec what is the rate of increase of its circumference ? 1. 0. 7 cm/sec 2. 0. 5π cm/sec 3. 2π cm/sec 4. π cm/sec |
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Answer» Correct Answer - Option 4 : π cm/sec Concept: Rate of change of 'x' is given by \(\rm \frac {dx}{dt}\) Circumference of circle = 2πr
Calculation: Here, \(\rm \frac {dr}{dt}\) = 0.5 cm/sec Circumference of circle, C = 2πr Now taking derivatives on both sides, we get \(\rm \frac {dC}{dt}\) = 2π \(\rm \frac {dr}{dt}\) = 2π (0.5) = π cm/sec Hence, option (4) is correct. |
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