Verified Answer :

  • Convert the board's total length from feet to inches: \(3 \text{ feet} \times 12 \text{ inches/foot} = 36 \text{ inches}\).
  • Divide the total length by the number of equal pieces: \(36 \text{ inches} / 6 = 6 \text{ inches}\).
  • The length of each piece is \(\boxed{6 \text{ inches}}\), which corresponds to option b.

Explanation

  1. Problem Analysis and Data Conversion

We are given a board that is \(3\) feet long. This board is cut into \(6\) equal pieces. We need to find the length of each of these pieces in inches. First, we need to convert the total length of the board from feet to inches, knowing that \(1\) foot equals \(12\) inches. Once we have the total length in inches, we can divide it by the number of pieces to find the length of each individual piece.

  1. Calculation and Result Interpretation

The total length of the board is \(3\) feet. Since \(1\) foot is equivalent to \(12\) inches, the total length in inches is given by:
\[3 \text{ feet} \times 12 \frac{\text{inches}}{\text{foot}} = 36 \text{ inches}.\]
Now, we divide this total length by the \(6\) equal pieces:
\[\frac{36 \text{ inches}}{6 \text{ pieces}} = 6 \text{ inches per piece}.\]
Thus, each piece is \(6\) inches long. This matches option b.

Examples

In construction, if you have a piece of wood that is 3 feet long and you need to cut it into 6 identical decorative supports for a shelf, this calculation helps you ensure each support is exactly 6 inches, guaranteeing the final structure is level and professional. Applying unit conversions like feet to inches is a foundational skill in DIY projects, interior design, and carpentry.

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