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Expert-verified Found in: Page 480 ### Geometry

Book edition Student Edition
Author(s) Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen
Pages 227 pages
ISBN 9780395977279 # A rectangular beam of wood 3 m long is cut into 6 pieces. Find the volume of each piece in cubic centimetres.

The volume of each piece is$21600{\text{\hspace{0.17em}\hspace{0.17em}cm}}^{3}$ .

See the step by step solution

## Step 1. Given information.

A rectangular beam of wood 3 cm long is cut into six pieces.

The figure provided in the question, ## Step 2. Determine the base.

Firstly, find the base area of rectangular beam.

The dimensions of rectangular beam are

$\begin{array}{c}8+8+8=24\text{\hspace{0.17em}cm,}\\ 6+6+6=18\text{\hspace{0.17em}cm}\end{array}$

Then, the base area is:

$24×18=432{\text{\hspace{0.17em}\hspace{0.17em}cm}}^{2}$

## Step 3. Determine the volume.

The volume of beam is:

$\begin{array}{c}v=Bh\\ =432×300\text{[substitute]}\\ =129600{\text{\hspace{0.17em}\hspace{0.17em}cm}}^{3}\text{[multiply]}\end{array}$

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

$\begin{array}{c}v\text{'}=\frac{v}{6}\\ =\frac{129600}{6}\text{[substitute]}\\ =21600{\text{\hspace{0.17em}\hspace{0.17em}cm}}^{3}\text{[divide]}\end{array}$

Thus, the volume of each piece is$21600{\text{\hspace{0.17em}\hspace{0.17em}cm}}^{3}$ . ### Want to see more solutions like these? 