Surface Areas and Volumes | Class 10 Mathematics Notes

12.2 Surface Area of a Combination of Solids

When dealing with solids formed by combining two or more basic solids, the surface area calculation requires careful consideration. The total surface area of the combined solid is not simply the sum of the surface areas of the individual solids because some surfaces become internal and are not visible after joining. To find the surface area of such a composite solid, we first break it down into its constituent parts whose surface areas we know how to calculate. For example, a container shaped like a cylinder with two hemispheres attached at the ends has a surface area equal to the sum of the curved surface area of the cylinder and the curved surface areas of the two hemispheres, excluding the circular areas where they join. Similarly, a toy formed by joining a cone and a hemisphere at their bases will have a total surface area equal to the curved surface area of the cone plus the curved surface area of the hemisphere, since the bases are joined and not exposed. The chapter provides detailed examples to illustrate these concepts, including calculating the surface area of a playing top shaped like a cone surmounted by a hemisphere, a decorative block made of a cube and a hemisphere, and a toy rocket shaped by combining a cone and a cylinder with different base diameters. These examples emphasize the importance of identifying which surfaces are exposed and which are hidden when calculating total surface area.

📊 Diagram: Fig. 12.2; Fig. 12.3; Fig. 12.4; Fig. 12.5; Fig. 12.6; Fig. 12.7; Fig. 12.8

🧪 Activity: Calculating the surface area of a toy shaped like a cone surmounted by a hemisphere using given dimensions.

🔗 Connection: Prepares for the next section which covers volume calculations of combined solids.