Question

A piece of wood is in the shape of a rectangular prism with a length of 10 inches, a width of 4 inches, and a height of 5 inches. You cut the wood in half to form two pieces of wood, each with a length of 5 inches. What is the percent increase in the total surface area? Round your answer to the nearest hundredth, if necessary. %

Answer 1

Answer: 18.18%

Explanation:

First, let's calculate the surface area of the original piece of wood. The surface area (SA) of a rectangular prism is given by the formula:

`$$SA = 2lw + 2lh + 2wh$$`

where
`\(l\)` is the length,
`\(l\)` is the width, and
`\(h\)` is the height. For the original piece of wood,
`\(l = 10\) inches`,
`\(w = 4\) inches`, and
`\(h = 5\) inches`.

After the piece of wood is cut in half, the length becomes 5 inches, but the width and height remain the same. So, for each of the two new pieces of wood,
`\(l = 5\) inches`,
`\(w = 4\) inches`, and
`\(h = 5\) inches`. The total surface area of the two new pieces of wood is twice the surface area of one of the new pieces.

The percent increase in the total surface area is given by the formula:

`$$\text{Percent Increase} = \frac{\text{New Total SA} - \text{Original SA}}{\text{Original SA}} * 100\%$$`

Let's calculate these values.

The percent increase in the total surface area when the piece of wood is cut in half is approximately 18.18%.