Answer:
1.333 cm/s
Explanation:
The formula for the volume of the cube V in term of its edge s is:
[tex]V = s^3[/tex]
By using chain rule we have the following equation between the rate of change of the volume and the rate of change of the edge:
[tex]\frac{dV}{dt} = \frac{dV}{ds}\frac{ds}{dt}[/tex]
[tex]100 = \frac{d(s^3)}{ds}\frac{ds}{dt}[/tex]
[tex]100 = 3s^2\frac{ds}{dt}[/tex]
[tex]\frac{ds}{dt} = \frac{100}{3s^2}[/tex]
We can substitute s = 5 cm:
[tex]\frac{ds}{dt} = \frac{100}{3*5^2} = 100 / 75 = 1.333 cm/s[/tex]
