The length of a side of a cube is increasing at a rate of 4 inches per second. At what rate is the surface area increasing when the volume of the cube is 216 square inches ?

1 Answer
Timber Lin
Apr 12, 2018

288 inches per second

Explanation:

#V=s^3# (volume of cube formula)

when #v=216#, #s=216^(1/3)=6#

#A=6s^2# (surface area)

differentiate #A=6s^2# with respect to #t# (time):
#(dA)/dt=12s(ds)/dt#
#(dA)/dt=12(6)(4)# (because side length increasing at 4 in/s)
#(dA)/dt=288# inches per second

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