What about irregular shapes?

The above examples were simplified through the approach of breaking them down into basic solids. Now, what happens if the object cannot be broken down into simple solids? For instance a mango, rocks, or sculptures; how will we find the curved surface area of these solids? Here, we use the concept of integration, where we break down an object into tiny rectangles and then add them up.

Surface Area of a Combination of Solids

All of us who study the chapters on surface area calculation have at least once wondered how to find the surface area of everyday objects like pencils, buckets, earthen pots and medicine capsules, isn’t it? Well, it isn’t as difficult as it seems- because these objects can be simplified as a combination of simple solid shapes. By the end of this article, you will thoroughly understand how to find the surface area of a combination of solids, right from the basics.

Table of Content

  • What is Surface Area?
    • Total Surface Area (TSA)
    • Curved Surface Area (CSA)
  • Surface Areas of Basic Solids
  • Surface Area of Combinations of Solids
  • Combination of Two Solids
  • Combination of Three Solids
  • Solved Problems on Surface Area of Combinations of Solids
  • What about irregular shapes?
  • Application in Real-Life Examples

Similar Reads

What is Surface Area?

Surface area is the total area occupied by the surface of a three-dimensional object. It is the sum of the areas of all the surfaces of the object....

Surface Areas of Basic Solids

Before we move to finding the surface area of a combination of solids, let us look quickly revise the formulae of some basic solids that we know:...

Surface Area of Combinations of Solids

The total surface area (TSA) of a combination of solids refers to the sum of the surface areas of all the individual solids involved. The formula for calculating the TSA depends on the specific combination of solids....

Combination of Two Solids

When you have a combination of two solids, such as a cylinder with a cone on top, or a cube with a hemisphere on one of its faces, calculating the total surface area involves finding the surface areas of each individual solid and then summing them up....

Combination of Three Solids

Now that we have seen the combination of two solids, let us look at a more complex topic: combination of three solids....

Solved Problems on Surface Area of Combinations of Solids

Example 1: Find the total surface area of a cylindrical tin can with a hemispherical lid. The radius of the cylindrical part is 5 cm and the height is 12 cm....

What about irregular shapes?

The above examples were simplified through the approach of breaking them down into basic solids. Now, what happens if the object cannot be broken down into simple solids? For instance a mango, rocks, or sculptures; how will we find the curved surface area of these solids? Here, we use the concept of integration, where we break down an object into tiny rectangles and then add them up....

Application in Real-Life Examples

Knowing the surface area of combination of solids can be very helpful in everyday-life as these combinations can be objects we use in real life as well. Some practical applications include:...

Conclusion

Surface area of a combination of solids is an important topic not just in mathematics, but also in many real-life situations. To recap, the easiest way to find the surface area of a combination of solids is to break down the object into fundamental solids, whose surface area is known to us. Here, we should be aware of which surfaces might be overlapping and redundant, and adjust our calculations accordingly. Many fields today use this fundamental concept to carry out the biggest of tasks and decisions....

Frequently Asked Questions about Combined Solids’ Surface Area

What is the meaning of surface area of solid?...