Cone volume: radius, diameter and slant height
Choose perpendicular height for volume and reserve slant height for the side surface.
Method
For a right circular cone, volume = πr²h ÷ 3. Radius is half the diameter. The height h is perpendicular from the base plane to the tip. Slant height runs along the side and equals √(r² + h²). It belongs in lateral area, πr × slant height, not in the volume formula.
Worked example
With diameter 6 cm and perpendicular height 4 cm, radius is 3 cm. Volume = π × 9 × 4 ÷ 3 ≈ 37.70 cm³, or 0.03770 litres. Slant height is 5 cm and lateral area is 15π ≈ 47.12 cm². A cylinder with the same radius and height has three times the cone’s volume.
What to check
Entering diameter as radius multiplies volume by four. Keep all dimensions in one length unit before calculating. An internal cone-shaped container needs internal dimensions and a known fill height; this formula assumes the straight-sided ideal shape.