Question

The volume of a cube increases at a rate of 4 m^3/sec. Find the rate at which the side of the cube changes when its length is 6 m. Submit an exact answer in fractional form. Provide your answer below: ds/dt = [ ] m/sec

          The volume of a cube increases at a rate of 4 m^3/sec. Find the rate at which the side of the cube changes when its length is 6 m.

Submit an exact answer in fractional form.

Provide your answer below:

ds/dt = [ ] m/sec

$The volume of a cube increases at a rate of 4 m^3/sec. Find the rate at which the side of the cube changes when its length is 6 m. Submit an exact answer in fractional form. Provide your answer below: ds/dt = [ ] m/sec$

Added by Joseph Z.

Calculus Volume 1

Gilbert Strang 1st Edition

Chapter 4

Instant Answer

Solved by Expert Donna Densmore

06/16/2024

Step 1

We are given that $ \frac{dV}{dt} = 4 \, m^3/sec $, and we want to find $ \frac{ds}{dt} $ when $ s = 6 \, m $. By the chain rule, $ \frac{dV}{dt} = \frac{dV}{ds} \cdot \frac{ds}{dt} $. Differentiating $ V = s^3 $ with respect to $ s $, we get \( Show more…

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