If the height of the first storey of a building is 3.20m and the riser is 13cm, the number of treads required is:
Try it first: pick an option, then read the explanation.
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