From Class IX, you are familiar with some of the solids like cuboid, cone, cylinder, and
sphere. You have also learnt how to find their surface areas and volumes. In our day-to-day life, we come across a number of solids made up of combinations
of two or more of the basic solids as shown above.
You must have seen a truck with a container fitted on its back, carrying oil or water from one place to another. Is it in the shape of any of the four basic solids mentioned above? You may guess that it is made of a cylinder with two hemispheres as its ends.
such a solid? Now, whenever we come across a new problem, we first try to see, if we can break it down into smaller problems, we have earlier solved. We can see that this solid is made up of a cylinder with two hemispheres stuck at either end. It would look like what we have in, after we put the pieces all together.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.
up of a combination of two basic solids. Here, we shall see how to calculate their
volumes. It may be noted that in calculating the surface area, we have not added the
surface areas of the two constituents, because some part of the surface area disappeared
in the process of joining them. However, this will not be the case when we calculate
the volume. The volume of the solid formed by joining two basic solids will actually be
the sum of the volumes of the constituents, as we see in the examples below.
Example 5 : Shanta runs an industry in a shed which is in the shape of a cuboid surmounted by a half cylinder.
We are sure you would have seen candles. Generally, they are in the shape of a cylinder. You may have also seen some candles shaped like an animal How are they made? If you want a candle of any special shape, you will have to heat the wax in a metal container till it becomes completely liquid. Then you will have to pour it into another container which has the special shape that you want. For example, take a candle in the shape of a solid cylinder, melt it and pour whole of the molten wax into another container shaped like a rabbit. On cooling, you will obtain a candle in the shape of the rabbit.
In Section 13.2, we observed objects that are formed when two basic solids were joined together. Let us now do something different. We will take a right circular cone and remove a portion of it. There are so many ways in which we can do this. But one particular case that we are interested in is the removal of a smaller right circular cone by cutting the given cone by a plane parallel to its base. You must have observed that the glasses (tumblers), in general, used for drinking water, are of this shape.
In this chapter, you have studied the following points:
1. To determine the surface area of an object formed by combining any two of the basic solids, namely, cuboid, cone, cylinder, sphere and hemisphere.
2. To find the volume of objects formed by combining any two of a cuboid, cone, cylinder, sphere and hemisphere.