Question

The volume of a cube with sides of length s is given by V = s^3. Find the rate of change of the volume with respect to s when s = 8 centimeters.​

Answer 1

Answer:

$V'(8)=192\text{ cm}^2$

Step-by-step explanation:

We have the volume of a cylinder:

$V=s^3$

To find the rate of change of the volume with respect to s, we will take the derivative of both sides with respect to s. So:

$\frac{d}{ds}[V]=\frac{d}{ds}[s^3]$

Differentiate. Use the power rule:

$V'(s)=3s^2$

So, to find the rate of change of the volume when s is 8 centimeters, substitute 8 for s:

$V'(8)=3(8)^2$

Evaluate:

$V'(8)=192\text{ cm}^2$