A sodium chloride crystal in the shape of a cube is expanding at the rate of 60 cubic microns per second. How fast is the side of the cube growing when the volume is 1000 cubic microns?

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Answer 1 · 2015-12-20T05:56:57

#1/5# #"microns/second"#

The sodium chloride is a cube.

#V=s^3#

Take the derivative with respect to time, #t#.

#(dV)/dt=3s^2(ds)/dt#

We know that:

#(dV)/dt=60#

We want to find #(ds)/dt# when #V=1000#, which means that #s=10#.

#60=3(10)^2(ds)/dt#

#60=300(ds)/dt#

#(ds)/dt=1/5# #"microns/second"#

When the cube has a volume of #1000# #"microns"^3#, the side of the cube is growing at a rate of #1/5# #"microns/second"#.