Calculate the area of insulation in square m required to cover a boiler drum which is equipped with hemispherical heads. The diameter of the drum is 84 cm and 4 m in length.

To accurately calculate the area of insulation required for a boiler drum with hemispherical heads, you first need to understand the shape and geometry involved.

The boiler drum can be seen as a cylinder with two hemispherical ends. The first step is to calculate the surface area of the cylindrical part of the drum, and then add the surface area of the two hemispherical heads.

1. Cylinder Surface Area: The formula for the lateral surface area of a cylinder is given by:

[

A_{\text{cylinder}} = 2 \pi r h

]

Where ( r ) is the radius and ( h ) is the height or length of the cylinder. Given the diameter of the drum is 84 cm, the radius ( r ) becomes 42 cm or 0.42 m. The length ( h ) of the drum is 4 m.

Substituting the values:

[

A_{\text{cylinder}} = 2 \pi (0.42 , \text{m}) (4 , \text{m}) = 10.560 , \text{m}^2

]

2. **Hemispherical Surface