Each edge of a cube is expanding at a rate of 4cm/s. How fast is the volume changing when each edge is 5cm? At what rate is the surface area changing when each edge is 7 cm?
Note, I'm using r for any one side on the cube rather than a radius
Yeah, it's an application of the chain rule.
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2. As the surface area is $\displaystyle A = 6r^2$ and $\displaystyle \frac{dr}{dt} = 4cm.s^{-1}$
this will be $\displaystyle \frac{dA}{dt} =(\frac{dA}{dr})(\frac{dr}{dt})$