Treatment Room Renovation: Countertop, Ramp, and Flooring
A dental office is renovating a treatment room with a rectangular floor measuring 4.8 m by 3.6 m. The designer plans a triangular corner cabinet in one corner, with the two straight edges along the walls measuring 1.2 m and 0.9 m. The countertop material costs $210 per square meter, and the installer requires 12% extra material for cuts and waste; sales tax is 7% on the material only. Separately, the office entrance has a threshold rise of 0.45 m. To meet accessibility guidelines, the ramp slope must not exceed 1:12 (vertical rise to horizontal run). The available horizontal run inside the entrance is only 5.0 m. The contractor proposes keeping the 5.0 m run and adding a small landing at the top. The office manager wants to know the total countertop cost, whether the ramp as proposed is compliant, and the flooring cost if the cabinet footprint is excluded from the flooring area.
1. Calculate the total countertop cost, including waste and sales tax.
Read the worked answer
The corner cabinet is a right triangle with legs 1.2 m and 0.9 m along the walls.
Area = ½ × base × height = ½ × 1.2 m × 0.9 m = 0.54 m².
Add 12% waste:
0.54 m² × 1.12 = 0.6048 m² of material to purchase.
Material cost before tax:
0.6048 m² × $210/m² = $127.008.
Sales tax:
$127.008 × 0.07 = $8.89056.
Total:
$127.008 + $8.89056 = $135.89856, which rounds to $135.90.
The waste allowance applies to the material purchase, not to the finished visible area, so using 0.54 m² alone would understate the cost.
2. Is the proposed ramp compliant? If not, what is the maximum rise for a 5.0 m run, and how much must the threshold be lowered?
Read the worked answer
A 1:12 slope means:
rise ÷ run ≤ 1/12, or run ≥ 12 × rise.
For a 0.45 m rise, the required run is:
12 × 0.45 m = 5.4 m.
The available run is only 5.0 m, so the proposed ramp is not compliant. Adding a landing at the top does not shorten the required ramp run; the 5.0 m ramp still has too steep a slope.
With a 5.0 m run, the maximum allowable rise is:
5.0 m ÷ 12 = 0.4167 m.
The threshold must be lowered by:
0.45 m − 0.4167 m = 0.0333 m ≈ 3.3 cm.
Alternatively, the run would need to be extended to 5.4 m, or the ramp would need to be redesigned with a different layout. Simply scheduling the landing does not fix the slope violation.
3. Calculate the flooring cost if the cabinet footprint is excluded, using flooring at $38 per square meter with 8% waste and 7% sales tax.
Read the worked answer
Room area:
4.8 m × 3.6 m = 17.28 m².
Cabinet footprint (triangle):
½ × 1.2 m × 0.9 m = 0.54 m².
Net flooring area:
17.28 m² − 0.54 m² = 16.74 m².
Add 8% waste:
16.74 m² × 1.08 = 18.0792 m².
Material cost:
18.0792 m² × $38/m² = $687.0096.
Sales tax:
$687.0096 × 0.07 = $48.090672.
Total:
$687.0096 + $48.090672 = $735.100272, which rounds to $735.10.
Excluding the cabinet saves the flooring cost on 0.54 m² plus its share of waste and tax, but the 8% waste allowance must still be applied to the remaining area.