Volume of a truncated cone calculator
Enter the dimensions of a truncated cone and read off its volume and surface area. Volumes convert to litres and gallons with the unit selector.
Volume
146.607 66m³
- Surface area
- 164.339 82
- Slant height
- 5.385 164 8
- Curved surface only
- 101.507 97
Show the working
- Bottom radius = 4
- Top radius = 2
- Height = 5
- Volume = pi * 5 / 3 * (4^2 + 4*2 + 2^2) = 146.608
- Surface area = pi * (4^2 + 2^2 + (4 + 2) * hypot(4 - 2, 5)) = 164.34
- Slant height = hypot(4 - 2, 5) = 5.385 16
- Curved surface only = pi * (4 + 2) * hypot(4 - 2, 5) = 101.508
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- volume = (pi h / 3)(R^2 + R r + r^2)
- slant height = sqrt((R - r)^2 + h^2)
- lateral surface = pi (R + r) l
A bucket, a lampshade and a plant pot are all frustums.
Switch the volume unit to litres or US gallons to read the capacity directly.