Surface Areas and Volumes | Class 10 Mathematics Notes

12.3 Volume of a Combination of Solids

Calculating the volume of solids formed by combining two or more basic solids involves adding the volumes of the individual parts because the volume occupied by the combined solid is the sum of the volumes of its constituents. Unlike surface area, where some surfaces become internal and hidden, volume is additive since the entire space occupied by each part contributes to the total volume. For example, a shed shaped like a cuboid surmounted by a half-cylinder has a volume equal to the volume of the cuboid plus half the volume of the cylinder. Similarly, a juice glass shaped like a cylinder with a hemispherical raised portion at the bottom has an apparent capacity equal to the volume of the cylinder, but the actual capacity is less by the volume of the hemisphere. The chapter provides detailed examples including calculating the volume of a shed, the actual capacity of a glass with a hemispherical base, the volume of a toy shaped like a hemisphere surmounted by a cone, and the difference in volume between this toy and a circumscribing cylinder. These examples highlight the importance of understanding volume formulas for basic solids and the additive property of volume for combined solids.

📊 Diagram: Fig. 12.12; Fig. 12.13; Fig. 12.14

🧪 Activity: Calculating volume of combined solids by adding volumes of individual parts.

🔗 Connection: Prepares for exercises and problems involving surface areas and volumes of combined solids.