Question

A cylindrical pillar is 50 cm in diameter and 3.5 m in height. How much concrete is required to construct this pillar if concrete weighs 2.4 g per cubic cm?

Answer 1

To calculate the amount of concrete required to construct the cylindrical pillar, we first need to find the volume of the cylinder and then convert it to the necessary units.

1. **Calculate the radius of the cylindrical pillar:**
The diameter of the pillar is 50 cm, so the radius \( r \) is:
\[
r = \frac{d}{2} = \frac{50 \text{ cm}}{2} = 25 \text{ cm}
\]

2. **Height of the pillar:**
The height \( h \) of the pillar is given as 3.5 m. To work in consistent units, we convert height to centimeters:
\[
h = 3.5 \text{ m} = 350 \text{ cm}
\]

3. **Calculate the volume of the cylinder:**
The volume \( V \) of a cylinder is given by the formula:
\[
V = \pi r^2 h
\]
Substituting the values of \( r \) and \( h \):
\[
V = \pi (25 \text{ cm})^2 (350 \text{ cm})
\]
\[
V = \pi (625 \text{ cm}^2) (350 \text{ cm})
\]
\[
V = \pi (218750 \text{ cm}^3)
\]
\[
V \approx 3.14159 \times 218750 \text{ cm}^3 \approx 686.4 \times 10^3 \text{ cm}^3 \approx 686400 \text{ cm}^3
\]

4. **Calculate the weight of the concrete:**
The weight is given by the volume multiplied by the density. The density of concrete is 2.4 g/cm³:
\[
\text{Weight} = V \times \text{Density} = 686400 \text{ cm}^3 \times 2.4 \text{ g/cm}^3
\]
\[
\text{Weight} = 1647360 \text{ g}
\]
To convert to kilograms:
\[
\text{Weight} = \frac{1647360 \text{ g}}{1000} = 1647.36 \text{ kg}
\]

Therefore, the amount of concrete required to construct the pillar is approximately **1647.36 kg**.