Chapter 4.7, Problem 28E

To determine

Whether the claim is correct.

Answer to Problem 28E

The claim is not correct.

Explanation of Solution

Given information:

The volume of a cube with side length $x$ is given by $V\left(x\right)=x^3$ , claims that when divide the volume in half, the volume decreases by a greater amount then when divide each side length in half.

Calculation:

The volume of cube with side $x$ is,

  $V\left(x\right)=x^3$

After dividing volume in half,

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

Now dividing side length in half,

  $\begin{array}{c}V\left(\frac{x}{2}\right)={\left(\frac{x}{2}\right)}^3\\ =\frac{x^3}{8}\end{array}$

Because $\frac{x^3}{2}>\frac{x^3}{8}$ , so the claim is not correct.