Calculations in an oblique circular cone. This is a cone, where the apex isn't perpendicular above the base center. The deviation d is the horizontal distance of apex and base center. Enter the base radius and two of the three values h, d and l. Choose the number of decimal places and click Calculate. Angles are calculated and displayed in degrees, here you can convert angle units. The lateral surface is calculated with an integral and can only be estimated here. The estimation is the better, the larger d is compared to r and h, so the more oblique the cone is.
α = arccos [ ( d² + l² - h² ) / ( 2 * d * l ) ]
β = arccos [ ( (d-r)² + m² - h² ) / ( 2 * (d-r) * m ) ]
if d = r: β = 90°
γ = arccos [ ( (d+r)² + n² - h² ) / ( 2 * (d+r) * n ) ]
L ≈ 2 * r * d, for d / ( r + h ) → ∞
π
L = r *
∫
√ [ r - d * cos(α) ]² + h² dα
0
B = π * r²
V = 1/3 * B * h
Radius, height, deviation and lenghts have the same unit (e.g. meter), lateral and base surface have this unit squared (e.g. square meter), the volume has this unit to the power of three (e.g. cubic meter). The lateral surface is the curved part of the surface area.