Cone Volume Calculator

Interpreted per the measurement selector above.
The smaller, flat end of a truncated cone.
Give this or the slant height.
Distance up the sloping face. Give this or the perpendicular height.
Material density for a solid cone, or contents density for a hopper.
Volume
37.699112
Cone Calculator
Slant height
5
Perpendicular height
4
Base radius
3
Top radius
0
Base area
28.274334
Top area
0
Lateral (curved) surface area
47.12389
Total surface area
75.398224
Half (taper) angle
36.869898 deg
Full apex / included angle
73.739795 deg
Height of the completed cone
4
Volume (cubic metres)
0.000038 m3
Volume (litres)
0.037699 L
Volume (US gallons)
0.009959 gal
Volume (cubic feet)
0.001331 ft3
Total surface area (square metres)
0.00754 m2
Worked out from Weisstein, Eric W. "Cone." MathWorld — A Wolfram Web Resource and 2 other sources.

How this is worked out

6 steps
  1. Radius r = 3 cm, height h = 4 cm
  2. Slant height l = sqrt(r^2 + h^2) = sqrt(9 + 16) = 5 cm
  3. Volume V = pi r^2 h / 3 = pi x 9 x 4 / 3 = 37.699112 cm^3
  4. Curved surface = pi (R + r) l = 47.12389 cm^2
  5. Total surface = curved + base = 75.398224 cm^2
  6. Taper half angle = atan((R - r)/h) = 36.869898 deg

Results are general information, not financial, tax, legal, medical or engineering advice.