Mathematics - Application of Derivative Question with Solution | TestHub

MathematicsApplication of DerivativeRate MeasureEasy2 minPYQ_2018

MathematicsEasysingle choice

A football is inflated by pumping air in it. When it acquires spherical shape its radius increases at the rate of $0.02 cm / s$ . The rate of increase of its volume when the radius is $10 cm$ is $π cm / s$

Options:

Answer:

Solution:

$v = \frac{4}{3} π r^{3} \frac{dv}{dt} = \frac{4}{3} π \frac{d}{dt} r^{3} = \frac{4}{3} π 3 r^{2} \cdot \frac{dr}{dt} = 4 π r^{2} \cdot \frac{dr}{dt}$ when $r = 10 cm$ ; $\frac{dv}{dt} = 4 π (10)^{2} \cdot (0.02) = 8 π cm^{3} / s$

Stream:VITEEESubject:MathematicsTopic:Application of DerivativeSubtopic:Rate Measure

⏱ 2mℹ️ Source: PYQ_2018

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