Chapter 4.7, Problem 28E

To determine

To find: whether the volume decrease when the volume of cube is divided by half is greater decreases than each side of the cube is half.

Answer to Problem 28E

Friend is not right.

Explanation of Solution

Given:

Volume of the cube:

  $V\left(x\right)=x^3$ .

Concept used:

Volume of the when divide by $2$ it is only divide by $2$ but when all side of the cube is divided by $2$ means the same volume is divided by $8$ which the volume is decrease higher in the case of side is divided by $2$ .

Volume of the cube is $a^3$ .

Calculation:

The volume of the cube is:

  $V\left(x\right)=x^3$ .

When the volume is divided by $2$ or make the half of original volume:

  $V_2=\frac{V_1}{2}$ .

When the length of each side of the cube is divided by $2$ or half of each sides.

  $\begin{array}{l}{V}_1=x^3.\\ V_2=\left(\frac{x}{2}\right).\left(\frac{x}{2}\right).\left(\frac{x}{2}\right).\\ V_2=\frac{1}{8}.{\left(x\right)}^3.\\ V_2=\frac{1}{8}{V}_1.\end{array}$

The decrease in the volume When the length of each side of the cube is divided by $2$ is greater amount then When the volume is divided by $2$ or make the half of original volume:

Hence, friend is not right.