Chapter 14.4, Problem 46AYU

To determine

To find: The instantaneous rate of change of the volume of a cube of side $x$ meters with respect to the side $x$ $r$ at $x=3$.

Answer to Problem 46AYU

Solution:

$27$

Explanation of Solution

Given:

Volume of cube: $V=V\left(x\right)=x^3$.

$x=3$

Formula Used:

The instantaneous rate of change of volume $V$ of a cube with respect to side $x$ is given by $\frac{dV}{dx}$.

Calculation:

Here, $V=V\left(x\right)=x^3$.

$V\text{'}\left(x\right)=\frac{dV}{dx}=\frac{d}{dx}\left(x^3\right)$

$V\text{'}\left(x\right)=3x^2$

At $x=3$, we get;

$V^{\prime }\left(3\right)=3.\left(3^2\right)$

$V\text{'}\left(3\right)=27$