Find the volume of a composite solid by adding or subtracting the volumes of its parts.
📘 Example ① (Addition)
Find the volume of a composite solid formed by placing a cone with the same base on top of a cylinder with a base radius of 3 cm and a height of 6 cm (height of the cone: 4 cm).
Answer: Cylinder part = π×9×6 = 54π cm³.
Cone part = (1/3)×π×9×4 = 12π cm³.
Total = 54π + 12π = 66π cm³
Find the volume of a composite solid formed by placing a cone with the same base on top of a cylinder with a base radius of 3 cm and a height of 6 cm (height of the cone: 4 cm).
Answer: Cylinder part = π×9×6 = 54π cm³.
Cone part = (1/3)×π×9×4 = 12π cm³.
Total = 54π + 12π = 66π cm³
📘 Example ② (Subtraction)
Find the volume of the solid obtained by removing a cylinder with a base radius of 3 cm and a height of 10 cm from a cube with side length 10 cm.
Answer: Cube = 10³ = 1000 cm³. Cylinder = π×9×10 = 90π cm³.
Remaining volume = 1000 - 90π cm³
Find the volume of the solid obtained by removing a cylinder with a base radius of 3 cm and a height of 10 cm from a cube with side length 10 cm.
Answer: Cube = 10³ = 1000 cm³. Cylinder = π×9×10 = 90π cm³.
Remaining volume = 1000 - 90π cm³
💡 Key Point
- Composite solids are formed by addition (combining) or subtraction (removing)
- Calculate the volume of each part accurately before combining them
Practice Problems
- Find the volume of a composite solid formed by placing a regular square pyramid with the same base on top of a cube with side length 6 cm (height of the pyramid: 4 cm).
Answer and Explanation
- Answer: 264 cm³. Cube=216. Square pyramid=(1/3)×36×4=48. Total=264.