# The volume of a cube is increasing at the rate of 1200 cm³/min at the instant its edges are 20 cm long. At what rate are the edges changing at that in

The volume of a cube is increasing at the rate of $$1200\ cm\ \frac{sup}{min}$$ at the instant its edges are 20 cm long. At what rate are the edges changing at that instant?

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aprovard

The volume of a cube with edge length ee is given by:
$$\displaystyle{V}={e}^{{3}}$$
Differentiate with respect to t: $$\frac{dV}{dt}=3e^2(\frac{de}{dt})$$
Substitute $$\frac{dV}{dt}=1200\ \frac{cm^3}{min}$$ and $$e=20$$ cm then solve for $$\frac{de}{dt}:$$ $$\displaystyle{1200}={3}{\left({20}\right)}^{{2}}\cdot{\left({}\frac{{de}}{{\left.{d}{t}\right.}}\right)}$$
$$\displaystyle{1200}={1200}{\left({}\frac{{de}}{{\left.{d}{t}\right.}}\right)}$$
$$\displaystyle{1}={}\frac{{de}}{{\left.{d}{t}\right.}}$$
or
$$\displaystyle{}\frac{{de}}{{\left.{d}{t}\right.}}={1}{}\frac{{cm}}{\min}$$