Find the height using the Pythagorean theorem, then calculate the volume.
📘 Example ①
Find the volume of a regular square pyramid with a square base of side length 6cm and a slant height of 5cm.
Answer:Diagonal of the base/2 = 3√2 cm. h² = 25 - 18 = 7. h = √7 cm.
Volume = (1/3) × 36 × √7 = 12√7 cm³
Find the volume of a regular square pyramid with a square base of side length 6cm and a slant height of 5cm.
Answer:Diagonal of the base/2 = 3√2 cm. h² = 25 - 18 = 7. h = √7 cm.
Volume = (1/3) × 36 × √7 = 12√7 cm³
💡 Key Point
- Find the height using the Pythagorean theorem → substitute it into the volume formula
- Keep √ in the calculation until the end
Practice Problem
- Find the volume of a cone with a base radius of 3cm and a slant height of 5cm (you may leave the answer in terms of π).
Answer and Explanation
- Answer:12π cm³. h² = 5²-3² = 16. h=4. Volume=(1/3)×9π×4=12π.