Oh, dude, a cone has just one plane. Like, imagine slicing through an ice cream cone - you'd get one flat surface, right? So yeah, just the one plane for our delicious geometric treat.
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A true mathematical cone has none. Conventional cones have a circular plane at one end.
If it is a right circular cone, it has an infinite number of planes of symmetry. If it is an oblique circular cone, it has one plane of symmetry.
A cone has infinitely many symmetries. This is because a cone can be rotated about its axis an infinite number of times and still look the same. Additionally, a cone also has rotational symmetry, meaning that it looks the same when rotated by any multiple of 360 degrees.
There are many possible answers. Some are: A sphere or ellipsoid sliced by two planes A cone sliced by two planes A toroid (doughnut) with a wedge cut out An infinite circular prism sliced by two planes.
A cylinder and a cone have infinitely many planes of symmetry because of the circular face. However, a cylinder can also be cut in half lengthwise (imaging cutting a soda can in half), while a cone cannot (imagine cutting a ice cream cone in half). Therefore, a cylinder has one more plane of symmetry than a cone.
A frustum of a cone, or a sphere sliced by two planes are a couple of examples.