Cones
Volume and surface area of a cone.
Key idea
Volume and surface area of a cone.
In depth
A cone is a pyramid with a circular base. Its volume is one third of a cylinder with the same base and height: V = ⅓πr²h. The curved area is πrl, where l is the slant height, l² = r² + h².
Worked example
r = 3, h = 4: slant l = 5, V = ⅓π(9)(4) = 12π, curved area = 15π.
Formula
Real-world uses
- Working out the volume of an ice cream cone or a funnel
- Sizing a conical pile of gravel
Common mistake
Using height in place of slant height in the area.
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 Cones?
Volume and surface area of a cone. It is a topic at the advanced level in Geometry.
What is the formula for Cones?
The key formula is V = ⅓πr²h.
Where is Cones used in real life?
Real-world examples: Working out the volume of an ice cream cone or a funnel; Sizing a conical pile of gravel.
What should I learn before Cones?
Make sure you are comfortable with Cylinders: Surface Area, the previous topic in Geometry.
What is a common mistake with Cones?
Using height in place of slant height in the area.
How can I practise Cones?
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 Cones?
Move on to Pyramids 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.