Volume of a pyramid (including a polygonal pyramid or cone) = 1/3 × base area × height
It is 1/3 of the volume of a prism with the same base area and height.
📘 Example ①
Find the volume of a regular square pyramid with a square base of side length 6 cm and a height of 4 cm.
Answer: Base area = 36 cm². Volume = (1/3)×36×4 = 48 cm³
Find the volume of a regular square pyramid with a square base of side length 6 cm and a height of 4 cm.
Answer: Base area = 36 cm². Volume = (1/3)×36×4 = 48 cm³
📘 Example ② (Cone)
Find the volume of a cone with a base radius of 3 cm and a height of 4 cm.
Answer: Base area = π×9 = 9π cm². Volume = (1/3)×9π×4 = 12π cm³
Find the volume of a cone with a base radius of 3 cm and a height of 4 cm.
Answer: Base area = π×9 = 9π cm². Volume = (1/3)×9π×4 = 12π cm³
💡 Key Point
- Volume of a pyramid = (1/3) × base area × height
- It is 1/3 of the volume of a prism
Practice Problems
- Find the volume of a cone with a base radius of 6 cm and a height of 5 cm (leave π as it is).
Answer and Explanation
- Answer: 60π cm³. Base area=36π. Volume=(1/3)×36π×5=60π.