knightwandererx21 knightwandererx21

23-07-2021
Mathematics

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If the volume of the expanding cube is increasing at the rate 24 cm3 / min , how fast is its surface area increasing when the surface area is 216 cm2 ?

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Аноним Аноним

01-08-2021

Answer:

16 cm^2/min

Step-by-step explanation:

dV/dt=24

V=a^3, differentiate with respect to t

dV/dt=3a^2*da/dt, a^2*da/dt=8

S=6a^2, 216=6a^2. a=6. da/dt=(8/36)

dS/dt=12*a*da/dt=12*(8/6)=16 cm^2/min

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