Question

A steel beam that is 12 meters long is cut into four equal parts. The cross sections are rectangles with side lengths of 1 meter and 2 meters.

(c) What is the volume of the original beam?

Answer 1

Hint: Identify the shape of the beam & then use the formula to find its volume.

Step 1: A steel prism is a rectangular prism. Given the side lengths as 1 meter & 2 meters & the height of the bar is 12 meters.

Step 2: The formula of volume of rectangular prism is given as: $V=(B\times h)$

Where $B$ is the base area and $h$ is the height of the rectangular prism.

Now the base of the steel prism is rectangular in shape.

So, $B=l\times w$

Where $l$ is the length & $w$ is the width of the rectangle.

Step 3: Here, $l=1\&w=2$

Substitute the values in the formula, We get

$B=(l\times 2)$

Now, Let’s find the volume,

$$\begin{gathered} V=(1\times 2)·12 \\ V=24 \end{gathered}$$

Hence, The volume of the original beam is 24 cubic meters.