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.

Question

asked May 7, 2021 41.2k views

1 Answer

Prosunjit Biswas · Answer 1 · 2021-05-11T10:09:27+0000

Answer:

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

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:

(d)/(ds)[V]=(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:

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