The volume of a cube with sides of length $s$ $s$ is given by $V = s^{3}$ $V =s^3$ . What is the rate of change of the volume with respect to $s$ $s$ when $s$ $s$ is 6 centimeters?

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The volume of a cube with sides of length $s$ $s$ is given by $V = s^{3}$ $V =s^3$ . What is the rate of change of the volume with respect to $s$ $s$ when $s$ $s$ is 6 centimeters?

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Answer 1 · 2018-06-02T11:36:23

$108 c m^{3}$ $color(blue)(108cm^3)$

Explanation:

We are given the volume function:

$V = s^{3}$ $V=s^3$

The rate of change is found using the first derivative of this function. This is often called the gradient function, because it gives the gradient of a tangent line drawn at the specified point.

$\frac{d V}{d s} (s^{3}) = 3 s^{2}$ $(dV)/(ds)(s^3)=3s^2$

We now plug in $s = 6$ $s=6$

$3 s^{2} = 3 {(6)}^{2} = 108 \frac{c m^{3}}{s}$ $3s^2=3(6)^2=108(cm^3)/s$

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The volume of a cube with sides of length $s$ $s$ is given by $V = s^{3}$ $V =s^3$ . What is the rate of change of the volume with respect to $s$ $s$ when $s$ $s$ is 6 centimeters?

1 Answer

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The volume of a cube with sides of length $s$ $s$ is given by $V = s^{3}$ $V =s^3$ . What is the rate of change of the volume with respect to $s$ $s$ when $s$ $s$ is 6 centimeters?