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

Efan Halliday 2021-05-19 Answered

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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Expert Answer

aprovard
Answered 2021-05-20 Author has 11117 answers

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
\(\displaystyle{}\frac{{de}}{{\left.{d}{t}\right.}}={1}{}\frac{{cm}}{\min}\)

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