Question

Find the volume and the lateral area of concrete column in the form of a right prism whose base is a regular hexagon of side 50 cm and whose altitude is 10m.

Answer 1

Given that the concrete column is in the form of a right prism with a hexagonal base, the formula for the volume is given below:

`\begin{gathered} \frac{3\sqrt[]{3}}{2}a^2h \\ \text{where a=50cm}=((50)/(100))m=0.5m \\ h=10m \end{gathered}`

The volume of the concrete column would be:

`\begin{gathered} \frac{3\sqrt[]{3}}{2}*0.5^2*10m \\ =6.495m^3 \end{gathered}`

To get the lateral area, the lateral area is given by:

`\begin{gathered} \text{Lateral area=}6ah \\ \text{where a is the side and h is the height} \\ \text{Lateral area = }6*0.5m*10m \\ \text{Lateral area = }30m^2 \end{gathered}`

Hence, the volume of the concrete column is 6.495 cubic metres and the lateral area is 30 square metres.