Chapter 12.5, Problem 29WE

To determine

To find: Theheight of the top piece.

Answer to Problem 29WE

The height of top piece is $6\sqrt[3]{4}$ .

Explanation of Solution

Given information:

The given figure is shown below.

  

Calculation:

Consider that a plane to the base of a pyramid separates the pyramid into two pieces with equal volumes.

Lets the volume of top part of the pyramid is $V_1$ and the volume of whole pyramid $V_2$ .

  $\begin{array}{c}\frac{V_1}{V_2}={\left(\frac{x}{12}\right)}^3\\ \frac{1}{2}={\left(\frac{x}{12}\right)}^3\\ \frac{x}{12}=\frac{1}{\sqrt[3]{2}}\\ x=\frac{12}{\sqrt[3]{2}}\end{array}$

The height of top piece is $x=6\sqrt[3]{4}$ .

Therefore, the height of top piece is $6\sqrt[3]{4}$ .