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The problem describes a staircase designed with cylindrical steps, each with a diameter of 30 cm and a total height of 1.5 meters. The task is to determine the mass of concrete needed to build the staircase, assuming a concrete density of 2.4 g/cm³.

### Step-by-step solution:

1. **Identify the number of cylinders:**
   The total height of the staircase is 1.5 meters, and there are 5 steps shown in the image. Each step can be represented as a cylinder.

2. **Convert units for consistency:**
   - Diameter of each step: \( D = 30 \, \text{cm} = 0.3 \, \text{m} \)
   - Height of each step: The total height of 1.5 meters must be divided by the 5 steps, so each step has a height of:
     \[
     h_{\text{step}} = \frac{1.5 \, \text{m}}{5} = 0.3 \, \text{m}
     \]
     In centimeters, this is \( h_{\text{step}} = 30 \, \text{cm} \).

3. **Volume of a single step (cylinder):**
   The volume of a cylinder is given by:
   \[
   V_{\text{cylinder}} = \pi r^2 h
   \]
   where:
   - \( r = \frac{D}{2} = 15 \, \text{cm} \) (radius of the cylinder)
   - \( h = 30 \, \text{cm} \) (height of each step)

   Thus, the volume of one step is:
   \[
   V_{\text{step}} = \pi (15)^2 (30) \, \text{cm}^3
   \]
   Let's calculate this.

4. **Total volume for 5 steps:**
   Since there are 5 steps, the total volume is:
   \[
   V_{\text{total}} = 5 \times V_{\text{step}}
   \]

5. **Mass of the concrete:**
   The mass of the concrete is determined using the formula:
   \[
   \text{Mass} = \text{Density} \times \text{Volume}
   \]
   The density of concrete is given as 2.4 g/cm³, so we will use this density to find the total mass.

Let me perform the necessary calculations.The total mass of concrete required to build the staircase is approximately **254.47 kg**.

Would you like further details or clarifications?

Here are 5 related questions to deepen your understanding:
1. How would the mass change if the number of steps were increased to 6?
2. What would the effect be if the density of the concrete was lower, say 2.2 g/cm³?
3. How could you calculate the total cost of the concrete, given the price per kilogram?
4. How would the mass be affected if the height of each step was reduced by 10 cm?
5. How can the volume of irregularly shaped structures (non-cylindrical) be calculated?

**Tip:** Always ensure unit consistency when solving real-world problems involving measurements.

Si un arquitecto diseña una escalera con huellas en forma de cilindros, y considera que cada cilindro de concreto debe tener el mismo diámetro (D=30cm) y altura. ¿Cuál es la masa de concreto que necesitaría para su ejecución? (considere que un tipo de concreto tiene una densidad de 2,4g/cm³)

Learn how to calculate the mass of concrete required for a staircase designed with cylindrical steps. This problem uses key geometry formulas for volume and mass, and includes unit conversions for consistency. Assumes a concrete density of 2.4 g/cm³.

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