Surface Area Of A Combination Of Solids


Imagine a container as shown in the diagram below.

In order to find the surface area of this container, let us consider different parts of it. We can see that this solid is made up of a cylinder with two hemispheres stuck at either end.

If we consider the surface of the newly formed object, we would be able to see only the curved surfaces of the two hemispheres and the curved surface of the cylinder.

So, the total surface area of the new solid is the sum of the curved surface areas of each of the individual parts. This gives,

TSA of new solid = CSA of one hemisphere + CSA of cylinder + CSA of other hemisphere

where TSA, CSA stand for ‘Total Surface Area’ and ‘Curved Surface Area’ respectively.

Imagine that we are trying to  make a toy by putting together a hemisphere and a cone. Let us see the steps that we would be going through.

First, we would take a cone and a hemisphere and bring their flat faces together. Here, of course, we would take the base radius of the cone equal to the radius of the hemisphere, for the toy is to have a smooth surface. So, the steps would be as shown in picture  below.

if we want to find how much paint we would require to colour the surface of this toy, we would need to know the surface area of the toy, which consists of the CSA of the hemisphere and the CSA of the cone.

So, we can say:

Total surface area of the toy = CSA of hemisphere + CSA of cone