A house has an entrance with two grand round columns supporting the roof.  The columns are 405 mm in diameter and 3 m high.  How much concrete would be required to build each one? Answer correct to two decimal places.

Use 3.14 as Pi

To calculate the volume of concrete required for each column, we can treat the columns as cylinders. The formula for the volume of a cylinder is:

\[
V = \pi r^2 h
\]

where:
- \(V\) is the volume,
- \(\pi = 3.14\),
- \(r\) is the radius of the base,
- \(h\) is the height of the cylinder.

### Given dataTo calculate the volume of concrete required for each column, we can treat the columns as cylinders. The formula for the volume of a cylinder is:

\[
V = \pi r^2 h
\]

where:
- \(V\) is the volume,
- \(\pi = 3.14\),
- \(r\) is the radius of the base,
- \(h\) is the height of the cylinder.

### Given 
- Diameter of the column = 405 mm = 0.405 m (since 1 m = 1000 mm),
- Radius \(r = \frac{0.405}{2} = 0.2025\) m,
- Height \(h = 3\) m.

### Plugging values into the formula:

\[
V = 3.14 \times (0.2025)^2 \times 3
\]

Let me calculate that for you.

\[
V = 3.14 \times 0.04100625 \times 3
\]
\[
V = 0.385456875 \, \text{m}^3
\]

Thus, the volume of concrete required for each column is approximately \(0.39\) cubic meters.

### Final Answer:
Each column requires approximately **0.39 m³** of concrete.

Would you like a breakdown of the steps or further details?

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**Related Questions:**
1. How would the volume change if the diameter of the column were doubled?
2. What if the height of the columns was increased to 4 meters?
3. How does the use of \( \pi = 3.14 \) affect the precision of the volume calculation?
4. How much concrete is required for both columns together?
5. What would the volume be if the columns had a hollow core?

**Tip:** Always remember to convert units to be consistent (e.g., mm to meters) when calculating volumes.

A house has an entrance with two grand round columns supporting the roof. The columns are 405 mm in diameter and 3 m high. How much concrete would be required to build each one? Answer correct to two decimal places. Use 3.14 as Pi.

Learn how to calculate the volume of concrete required for cylindrical columns with a diameter of 405mm and a height of 3 meters. This solution uses the formula for the volume of a cylinder and converts units for accurate results. Suitable for students in Grades 9-11.

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