Cone
Find the volume, slant height, lateral and total surface area of a cone and a frustum of a cone.
What is known:
Base radius r
x
Height h
x
Units:
Lengths are positive numbers (whole or decimal), angles are in degrees.
The cone calculator finds the volume, slant height, height or radius, base, lateral and total surface areas, the apex angle and the angle of the net of a cone, as well as the volume and surface of a frustum.
Cone formulas
| Value | Formula |
|---|---|
| Slant height | l = √(r² + h²) |
| Volume | V = ⅓πr²h |
| Base area | Sbase = πr² |
| Lateral surface area | Slat = πrl |
| Total surface area | S = πr(r + l) |
| Angle of the net | θ = 360° · r / l |
Example. r = 3 cm, h = 4 cm.
l = √(9 + 16) = 5 cm, V = ⅓π · 9 · 4 = 12π ≈ 37.7 cm³
Slat = π · 3 · 5 = 15π ≈ 47.12 cm², S = π · 3 · 8 = 24π ≈ 75.4 cm².
Frustum of a cone
| Slant height | l = √(h² + (R − r)²) |
| Volume | V = ⅓πh(R² + Rr + r²) |
| Lateral surface area | Slat = π(R + r)l |
The volume of a cone is one third of the volume of a cylinder with the same base and height.
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