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.
Cone and Hemisphere
This figure can be simplified into a cone and a hemisphere. But note that while calculating the curved surface area, we do not consider the base of the hemisphere and cone, as it is not exposed outside. Hence, we only add the curved surface area of the solids.
∴ S.A. of figure = C.S.A of cone + C.S.A of hemisphere
S.A. of figure = πrl + 2πr2
S.A. of figure = πr(l+2r)
Cylinder and Cone
For the total surface area of this solid, we need to take into account the curved surface area of the cylinder, the area of the base of the cylinder and the curved surface area of the cone (not TSA as the base of cone is inside the solid)
∴ S.A. of figure = CSA of cylinder + base area of cylinder + CSA of cone
S.A. of figure = 2πrh + πr2 + πrl
S.A. of figure = πr(2h + r + l)
Cylinder and Cube
Here, since there is an overlapped area of the top of the cylinder, here is how we calculate the surface area of this solid:
∴ S.A. of figure = (CSA of cylinder + area of base of cylinder + TSA of cube) – area of top of cylinder
S.A. of figure = (2πrh + πr2 + 6a2) – πr2
S.A. of figure = 2πrh + 6a2
Cone and Cube
Here, since there is an overlapped area of the top of the cone, here is how we calculate the surface area of this solid:
∴ SA of solid = (CSA of cone + TSA of cube) – area of top of cone
SA of solid = ( πrl + 6a2) – πr2
SA of solid = πr(l + r) + 6a2
Cube and Hemisphere
Here, since there is an overlapped area of the hemisphere, here is how we calculate the surface area of this solid:
∴ SA of solid = (SA of cube + SA of hollow hemisphere) – base area of hemisphere
SA of solid = (6a2 + 2πr2) – πr2
SA of solid = 6a2 + πr2
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
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