laishacruz011 laishacruz011

21-03-2020
Mathematics

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The volume of a spherical balloon is increasing at the rate of 25cm^3/min, how fast is the radius increasing when the radius is equal to 20cm?

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ultraman ultraman

21-03-2020

Answer:

V＝4/3πr^3；S＝4πr^10；dV/dt＝dV/dr×dr/dt＝4πr^10×dr/dt；dS/dt＝dS/dr×dr/dt＝8πr×dr/dt＝2/r×dV/dt；当r＝10cm时,dS/dt＝50cm^2/s

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