Q37. - Geometry

Question

A rectangular beam of wood 3 m long is cut into 6 pieces. Find the volume of each piece in cubic centimetres.

Step-by-Step Solution

Answer

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

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:

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

Step 3. Determine the volume.

The volume of beam is:

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

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$21600{\text{\hspace{0.17em}\hspace{0.17em}cm}}^3$ .