AoE: cone or arc?

[viaFAMILIAR]

Regarding the AoE of a "cone", is it a true conic or should it essentially be treated as an arc/triangle?

ie: if burning hands/dragon's breath is cast from above the battlefield, shouldn't it affect a 15' circle?

[stoutstien]

a cone is a cone, so yes if you use burning hands from 15 feet above the ground it would cause damage to every target in a a 15 foot circle on the ground

[MrStabby]

If directly above.

At an angle it s an ellipse.

More generally a conic section.

[Unoriginal]

The PHB has a drawing with the various AoE shapes, if it helps, but even without that it's stated that cone spells are literal cones.

[LordKarnox]

The PHB has a drawing with the various AoE shapes, if it helps, but even without that it's stated that cone spells are literal cones.
He askes if they are shooting from directly above(Like flying above them), should the AoE shape be circle cause they are shooting directly down? I say yes.

[PhoenixPhyre]

The perpendicular cross-section of a "cone" spell is a circle (not a rectangle) in real-space.

Now in the mapping of that to a grid, if you're truly preserving the non-euclidean metric (diagonals are the same length as the edges, making squares and circles isometric...nah, too much work.

If you shoot a X' cone straight down, it intersects with the ground in a circle with maximum diameter = X. More precisely--

let H be the distance you are from the ground.
Let X be the range of the cone.
Let R be the radius of the circle formed at the intersection.
Then R = H/2.

If you shoot it from an angle, it would intersect in a conic section (likely an ellipse of some eccentricity). But I'd rather not do that math.