Oblique Cut Cone Volume

From the radius and the two heights of the short and tall sides, work out the volume, lateral area, slanted elliptical top area and surface area of an obliquely cut cylindrical solid.

Input

Enter the radius and the two heights of the short and tall sides to compute the volume and more of an obliquely cut cylindrical solid.

Radius r

Short side height h1

Tall side height h2

Result

Volume

402.12386

Mean height

Lateral area

201.06193

Top area

56.198518

Surface area

307.52593

Lengths use the input unit, areas are squared and volume is cubed.

How it works

With radius r, short side height h1 and tall side height h2, the volume uses the mean height (h1 + h2) / 2 as V = π r² × (h1 + h2) / 2. An oblique cut keeps the same volume as a straight cylinder of that mean height.
The curved lateral area equals the base perimeter 2 π r times the mean height, that is π r (h1 + h2).
The slanted top is an ellipse with minor semi axis r and major semi axis l = √(r² + ((h2 − h1) / 2)²). Its area is π r l.
The surface area is the sum of the base circle π r², the lateral surface π r (h1 + h2) and the slanted top π r l.
Lengths use the same unit as the input, areas are squared and volume is cubed. When h1 equals h2 the solid matches an ordinary cylinder.

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