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A carpenter is working with a beam that is 10 feet long and in the shape of a rectangular prism. He cuts the beam in half. What happens to the surface area and the volume of the beam?

A Carpenter Is Working With A Beam That Is 10 Feet Long And In The Shape Of A Rectangular Prism He Cuts The Beam In Half What Happens To The Surface Area And Th class=
A Carpenter Is Working With A Beam That Is 10 Feet Long And In The Shape Of A Rectangular Prism He Cuts The Beam In Half What Happens To The Surface Area And Th class=

Sagot :

For this problem, we are provided with the image of a beam and its dimensions, we are then informed that the beam was cut in half, and we need to compare the surface area and volume of the beam before and after the cut.

The surface area of a rectangular prism can be calculated with the following expression:

[tex]A_{\text{surface}}=2\cdot(\text{width}\cdot\text{height}+\text{width}\cdot\text{length}+\text{height}\cdot\text{length)}[/tex]

The volume of a rectangular prism can be calculated with the following expression:

[tex]V=\text{width}\cdot\text{height}\cdot\text{length}[/tex]

We can use these formulas to calculate the characteristics of the beam before the cut:

[tex]\begin{gathered} A_{\text{surface}}=2\cdot(10\cdot1+1\cdot1+1\cdot10)=42\text{ square ft} \\ V=10\cdot1\cdot1=10_{}\text{ cubic ft} \end{gathered}[/tex]

Now we can calculate the characteristics of the beam after the cut:

[tex]\begin{gathered} A_{\text{surface}}=2\cdot(5\cdot1+1\cdot1+1\cdot5)=22\text{ square ft} \\ V=5\cdot1\cdot1=5\text{ cubic ft} \end{gathered}[/tex]

With this, we can conclude that:

The surface area of the cut beam is 20 sq ft smaller than the original beam.

The volume of the cut beam is half the volume of the original beam.