Checking a wheelchair ramp gradient and paint cost
A community centre needs a wheelchair ramp at its main entrance. The door threshold is 0.72 m above the pavement. The recommended maximum gradient is 1:12, meaning 1 unit of rise for every 12 units of horizontal run. The only available straight run along the front of the building is 8.00 m, measured horizontally, before the ramp would block a fire exit. The committee proposes extending the ramp 0.80 m into the car park, giving a horizontal run of 8.80 m. The ramp will be 1.20 m wide. A non-slip paint covers 5.0 m² per litre and must be applied in two coats. Paint is sold only in 1-litre tins at €24 each.
1. Calculate the minimum horizontal run needed for a 1:12 ramp. Decide whether the original 8.00 m run or the proposed 8.80 m run complies. Show your reasoning.
Read the worked answer
A gradient of 1:12 means horizontal run = 12 × rise.
Minimum run = 12 × 0.72 m = 8.64 m.
Original run: 8.00 m is less than 8.64 m, so it is too steep and does not comply.
Proposed run: 8.80 m is greater than 8.64 m, so it complies. The actual gradient is 0.72 : 8.80. Dividing both parts by 0.72 gives 1 : 12.22, which is flatter than 1 : 12.
The proposed 8.80 m ramp is acceptable on gradient, but extending into the car park may need checking against fire-exit access.
2. Calculate the sloping length of the 8.80 m ramp and the area to be painted. Determine how many 1-litre tins are needed for two coats and the paint cost.
Read the worked answer
The sloping length is the hypotenuse of a right triangle with horizontal run 8.80 m and rise 0.72 m.
Sloping length² = 8.80² + 0.72² = 77.44 + 0.5184 = 77.9584 Sloping length = √77.9584 ≈ 8.83 m.
Area of ramp surface = 8.83 × 1.20 ≈ 10.60 m². Two coats need 2 × 10.60 = 21.20 m² of coverage.
Paint needed = 21.20 ÷ 5.0 = 4.24 litres. Since paint is sold only in 1-litre tins, buy 5 tins.
Cost = 5 × €24 = €120.