What is the surface area of a pressure vessel in the form of a cylinder with hemispherical ends, if the overall length is 12 m and diameter is 3 m?

To determine the surface area of a pressure vessel shaped as a cylinder with hemispherical ends, we need to calculate both the cylindrical portion's surface area and the surface area of the two hemispheres.

1. Cylindrical Portion: The surface area of a cylinder (excluding the ends) is given by the formula:

[

A_{cylinder} = 2 \pi r h

]

where ( r ) is the radius and ( h ) is the height (or length) of the cylinder.

Given a diameter of 3 m, the radius ( r ) will be:

[

r = \frac{3}{2} = 1.5 , \text{m}

]

The overall length of the vessel is 12 m. However, we must subtract the lengths of the hemispherical ends to find the length of the cylindrical section. Each hemisphere has a height equal to its radius, which is 1.5 m, so the total length of the two hemispheres is:

[

2 \times 1.5 = 3 , \text{m}

]

This gives the effective height