Chapter 12.1, Problem 37WE

To determine

To find: the volume of each piece in cubic centimeters.

Answer to Problem 37WE

The volume of each piece is $21600{\text{cm}}^3$ .

Explanation of Solution

Given information:

A rectangular beam of wood $3\text{cm}$ long is cut into six pieces.

The figure provided in the question,

  

Calculation: to find the volume of each piece, first find the base area of rectangular beam,

The dimensions of rectangular beam are $8+8+8=24\text{cm,}6+6+6=18\text{cm}$ ,

Thus, the base area is,

  $24·18=432{\text{cm}}^2$

The volume of beam,

  $\begin{array}{l}v=Bh\\ v=432·300\text{ [substitute]}\\ v=129600{\text{cm}}^3\text{ [multiply]}\end{array}$

To find the each piece volume, divide the volume by six,

  $\begin{array}{l}v\text{'}=\frac{v}{6}\\ v\text{'}=\frac{129600}{6}\text{ [substitute]}\\ v\text{'}=21600{\text{cm}}^3\text{ [divide]}\end{array}$

Thus, the volume of each piece is $21600{\text{cm}}^3$ .