Calculate the volume, slant height, and surface area of a right circular cone from its radius and height.
A right circular cone is a 3D shape with a flat circular base that tapers smoothly to a single point (the apex) directly above the center of the base. It is fully defined by its base radius (r) and its height (h), the perpendicular distance from the base to the apex.
Slant Height: l = √(r² + h²)
Volume: V = (1/3) × π × r² × h
Lateral Surface Area: Alateral = π × r × l
Total Surface Area: Atotal = π × r × (r + l)
1. Enter the base radius (r) of the cone.
2. Enter the vertical height (h) of the cone.
3. Choose your unit and click Calculate to get the slant height, volume, and surface areas instantly.
For a cone with r = 3 cm and h = 8 cm:
Slant height l = √(9 + 64) = 8.54 cm
Volume = (1/3) × π × 9 × 8 = 75.40 cm³
Lateral area = π × 3 × 8.54 = 80.48 cm²
Total area = π × 3 × (3 + 8.54) = 108.75 cm²
Volume = (1/3) × π × r² × h; Lateral surface area = π × r × slant height; Total surface area adds the base circle area.
It's the distance from the cone's apex to the edge of its base along the surface, calculated as √(r² + h²) using the Pythagorean theorem.
A cone has a circular base and a single curved lateral surface; a pyramid has a polygonal base and flat triangular faces.