Cone Calculator
Calculate volume, total surface area, lateral area and slant height of a right cone.
Inputs
units
units
Volume
150.7964cu units
Total Surface Area
174.0299sq units
Lateral Area
123.7644sq units
Slant Height
9.8489units
Step by step
Slant height
l = √(4² + 9²)
= 9.8489
Volume
V = ⅓π × 4² × 9
= 150.7964
Lateral area
LA = π × 4 × 9.8489
= 123.7644
How it works
A right circular cone has volume (1/3)πr²h — exactly one-third of the cylinder with the same base and height. The slant height l = √(r²+h²).
Formulas
Volume
V = (1/3)πr²h
- r
- Base radius
- h
- Height
Lateral Area
LA = πrl
- r
- Base radius
- l
- Slant height
Frequently Asked Questions
Why is cone volume exactly 1/3 of a cylinder?
This can be proven via calculus (integration of circular cross-sections) or Cavalieri's principle.
What if I only know slant height and radius?
Height = √(l² − r²). The slant height, radius and height form a right triangle.