In construction, floor space must be given for staircases. If the second floor is 3.6 meters above the first floor and a contractor is using the standard step pattern of 28 cm of tread for 18 cm of rise then how many steps are needed to get from the first to the second floor and how much linear distance will need to be used for the staircase?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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In construction, [floor space must be given for staircases](#). If the second floor is 3.6 meters above the first floor and a contractor is using the standard step pattern of 28 cm of tread for 18 cm of rise, then how many steps are needed to get from the first to the second floor and how much linear distance will need to be used for the staircase?

### Explanation:
- **Rise**: The vertical height each step reaches (18 cm).
- **Tread**: The horizontal depth of each step (28 cm).

### Calculation:
1. **Number of Steps**:  
   To find the number of steps required, divide the total height by the rise of each step:
   \[
   \text{Number of Steps} = \frac{360 \, \text{cm}}{18 \, \text{cm/step}}
   \]
   Calculate the result to determine the number of required steps.

2. **Linear Distance**:  
   Multiply the number of steps by the tread to find the total horizontal distance:
   \[
   \text{Linear Distance} = \text{Number of Steps} \times 28 \, \text{cm}
   \]
   This gives the total linear distance of the staircase.
Transcribed Image Text:In construction, [floor space must be given for staircases](#). If the second floor is 3.6 meters above the first floor and a contractor is using the standard step pattern of 28 cm of tread for 18 cm of rise, then how many steps are needed to get from the first to the second floor and how much linear distance will need to be used for the staircase? ### Explanation: - **Rise**: The vertical height each step reaches (18 cm). - **Tread**: The horizontal depth of each step (28 cm). ### Calculation: 1. **Number of Steps**: To find the number of steps required, divide the total height by the rise of each step: \[ \text{Number of Steps} = \frac{360 \, \text{cm}}{18 \, \text{cm/step}} \] Calculate the result to determine the number of required steps. 2. **Linear Distance**: Multiply the number of steps by the tread to find the total horizontal distance: \[ \text{Linear Distance} = \text{Number of Steps} \times 28 \, \text{cm} \] This gives the total linear distance of the staircase.
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