Question

The volume of a cube is increasing at the rate

Solid Geometry
ANSWERED
asked 2021-08-09
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 instant?

Expert Answers (1)

2021-08-10

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 \(\frac{dV}{dt}=1200\ cm^3/min\) and e=20 cm then solve for 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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