A iron pillar consists of a cylindrical portion 2.8 m high and 20 cm in diameter and a cone 42 cm heigh is surmounting it. Find the weight of the pillar, given that `1 cm^(3)` of iron weight 7.5 g

Explanation

To find the weight of the iron pillar, we need to calculate the volume of both the cylindrical portion and the conical portion, and then use the density of iron to find the weight.

### Step-by-Step Solution:

1. **Convert Measurements to Consistent Units:**
- The height of the cylindrical portion is given as 2.8 m, which we convert to centimeters:
\[ 2.8 \, \text{m} = 2.8 \times 100 = 280 \, \text{cm} \]
- The diameter of the cylinder is 20 cm, so the radius \( r \) is:
\[ r = \frac{20}{2} = 10 \, \text{cm} \]
- The height of the conical portion is given as 42 cm.

2. **Calculate the Volume of the Cylinder:**
- The formula for the volume \( V \) of a cylinder is:
\[ V = \pi r^2 h \]
- Substituting the values:
\[ V_{\text{cylinder}} = \pi (10)^2 (280) = \pi (100) (280) = 28000\pi \, \text{cm}^3 \]

3. **Calculate the Volume of the Cone:**
- The formula for the volume \( V \) of a cone is:
\[ V = \frac{1}{3} \pi r^2 h \]
- Substituting the values:
\[ V_{\text{cone}} = \frac{1}{3} \pi (10)^2 (42) = \frac{1}{3} \pi (100) (42) = 1400\pi \, \text{cm}^3 \]

4. **Calculate the Total Volume of the Pillar:**
- The total volume \( V_{\text{total}} \) is the sum of the volumes of the cylinder and the cone:
\[ V_{\text{total}} = V_{\text{cylinder}} + V_{\text{cone}} = 28000\pi + 1400\pi = 29400\pi \, \text{cm}^3 \]

5. **Calculate the Weight of the Pillar:**
- Given that 1 cm³ of iron weighs 7.5 g, the total weight \( W \) of the pillar can be calculated as:
\[ W = V_{\text{total}} \times \text{weight per cm}^3 = 29400\pi \times 7.5 \, \text{g} \]
- Approximating \( \pi \approx 3.14 \):
\[ W \approx 29400 \times 3.14 \times 7.5 \]
\[ W \approx 29400 \times 23.55 \approx 692370 \, \text{g} \]

6. **Convert Weight to Kilograms:**
- Since 1000 g = 1 kg, we convert the weight:
\[ W \approx \frac{692370}{1000} \approx 692.37 \, \text{kg} \]

### Final Answer:
The weight of the iron pillar is approximately **692.37 kg**.