Pyramids
Volume is one third base times height.
Key idea
Volume is one third base times height.
In depth
A pyramid has a polygon base and triangular faces meeting at an apex. Its volume is one third of base area times height: V = ⅓Bh, because three pyramids fill a prism with the same base and height.
Worked example
A square-based pyramid with base 6 and height 4: V = ⅓ × 36 × 4 = 48.
Formula
Real-world uses
- Calculating the volume of a glass pyramid roof
- Historical architecture and design
Common mistake
Forgetting the ⅓.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Pyramids?
Volume is one third base times height. It is a topic at the advanced level in Geometry.
What is the formula for Pyramids?
The key formula is V = ⅓ B h.
Where is Pyramids used in real life?
Real-world examples: Calculating the volume of a glass pyramid roof; Historical architecture and design.
What should I learn before Pyramids?
Make sure you are comfortable with Cones, the previous topic in Geometry.
What is a common mistake with Pyramids?
Forgetting the ⅓.
How can I practise Pyramids?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Pyramids?
Move on to Spheres next.
Related advanced topics in Geometry
- Heron’s Formula – Triangle area from three sides.
- Regular Polygon Area – Use apothem and perimeter.
- Arc Length of a Circle – Part of the circumference.
- Sector Area – Part of the circle’s area.
- Central and Inscribed Angles – An inscribed angle is half the central angle on the same arc.
- Chord and Tangent Properties – A tangent is perpendicular to the radius at the point of contact.