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?

vangstosiis 2022-07-22 Answered
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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Answers (1)

Dominique Ferrell
Answered 2022-07-23 Author has 18 answers
The sodium chloride is a cube.
V = s 3
Take the derivative with respect to time, t.
d V d t = 3 s 2 d s d t
We know that:
d V d t = 60
We want to find d s d t when V=1000, which means that s=10.
60 = 3 ( 10 ) 2 d s d t
60 = 300 d s d t
d s d t = 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 .
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