If the height of the first storey of a building is 3.20m and the riser is 13cm, the number of treads required is:
🔬 Understanding the Concept: Risers, Treads, and Rounding
This problem again uses the fundamental relationship between risers and treads. However, it introduces a common real-world scenario where the total height is not a perfect multiple of the proposed riser height.
Riser: The vertical height of a single step. The total number of risers must cover the entire floor-to-floor height.
Tread: The horizontal depth of a step.
Important Rule: The number of risers must be a whole number. Since you cannot have a fraction of a step, you must round the calculated number of risers up to the next integer to ensure the staircase reaches the next floor.
⚖️ The Key Relationship
The core formulas for solving this are:
Number of Risers = RoundUp (Total Height / Riser Height)
Number of Treads = Number of Risers - 1
📋 Step-by-Step Calculation
Let's calculate the required number of treads using the given information.
- List the Given Data:
- Total Floor Height = 3.20 m
- Height of one Riser (Rise) = 13 cm
- Convert Units to be Consistent:
- Let's use centimeters (cm).
- Total Floor Height = 3.20 m * 100 cm/m = 320 cm
- Height of one Riser = 13 cm
- Calculate the Number of Risers:
- Number of Risers = (Total Floor Height) / (Height of one Riser)
- Number of Risers = 320 cm / 13 cm = 24.615...
- Since we must have a whole number of risers, we round this value up to the next integer: 25 Risers.
- (Note: This means the actual constructed riser height would be slightly adjusted to 320cm / 25 = 12.8cm to fit perfectly).
- Calculate the Number of Treads:
- Using the key formula: Number of Treads = Number of Risers - 1
- Number of Treads = 25 - 1
- Number of Treads = 24