rior wall of a small office building under construction is constructed of \( \frac{3}{4} \) in. paneling. \( \frac{5}{8} \) in. Firecode sheetrock, \( 3 \frac{3}{4} \) in. studs, \( \frac{1}{2} \) in. CDX plywood sheathing, \( 1 \frac{3}{4} \) i hoard, and \( \frac{5}{8} \) in. exterior surfacing. Calculate the total thickness of the wall. thickness of the wall is whole number, fraction, or mixed number. Simplify your answer.)

To calculate the total thickness of the wall, we'll add up the thicknesses of all the individual layers. Here's a step-by-step breakdown: ### Given Thicknesses: 1. **Paneling:** \( \frac{3}{4} \) inches 2. **Firecode Sheetrock:** \( \frac{5}{8} \) inches 3. **Studs:** \( 3 \frac{3}{4} \) inches 4. **CDX Plywood Sheathing:** \( \frac{1}{2} \) inch 5. **Board (Assumed from "hoard"):** \( 1 \frac{3}{4} \) inches 6. **Exterior Surfacing:** \( \frac{5}{8} \) inches ### Convert All Measurements to Eighths: To simplify the addition, we'll convert all measurements to eighths of an inch. 1. **Paneling:** \( \frac{3}{4} = \frac{6}{8} \) inches 2. **Firecode Sheetrock:** \( \frac{5}{8} \) inches 3. **Studs:** \( 3 \frac{3}{4} = \frac{15}{4} = \frac{30}{8} \) inches 4. **CDX Plywood Sheathing:** \( \frac{1}{2} = \frac{4}{8} \) inches 5. **Board:** \( 1 \frac{3}{4} = \frac{7}{4} = \frac{14}{8} \) inches 6. **Exterior Surfacing:** \( \frac{5}{8} \) inches ### Add All Thicknesses: \[ \frac{6}{8} + \frac{5}{8} + \frac{30}{8} + \frac{4}{8} + \frac{14}{8} + \frac{5}{8} = \frac{64}{8} \] ### Simplify: \[ \frac{64}{8} = 8 \text{ inches} \] ### **Total Thickness of the Wall:** **8 inches**