Calculate the volume, surface area, lateral area, and slant height of a cone from base radius and height.
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37.7
Volume
75.4
Surface area
47.12
Lateral area
5
Slant height
28.27
Base area
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Geometry
Calculate the volume, total surface area, lateral area, and slant height of a cone from its base radius and height.
Volume is one-third of a cylinder with the same base and height: V = (1/3) * pi * r^2 * h. The slant height is found using the Pythagorean theorem: l = sqrt(r^2 + h^2).
Lateral surface area = pi * r * l. Total surface area adds the base circle: SA = pi * r * (r + l).
V = (1/3) pi r^2 h
One-third of the cylinder volume.
l = sqrt(r^2 + h^2)
Slant height from radius and vertical height.
This calculator handles right circular cones only — not oblique cones or truncated cones (frustums).
Frequently asked questions
A cone tapers to a point. It can be proven geometrically (Cavalieri's principle) that exactly three cones fill a cylinder of the same base and height.
Use the Pythagorean theorem: slant = sqrt(radius^2 + height^2). The calculator computes this automatically.
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