When a square pyramid is sliced perpendicular to its base through a vertex, the cross section will be a triangle. This triangle will have one vertex at the apex of the pyramid and the other two vertices on the base, forming a triangular shape that includes one of the pyramid's edges and a segment of the base. The resulting triangle will be isosceles if the slice is made symmetrically.
Sphere
The vertical cross section of a square pyramid is a triangle. When the pyramid is sliced vertically through its apex and down to the base, the resulting shape is a triangular profile that includes the apex at the top and the edges of the base at the bottom. The height of the triangle corresponds to the height of the pyramid, while the base of the triangle spans the width of the base of the pyramid.
They would be two right triangular pyramids.
A sphere, a cone, a section of a sphere or ellipsoid, a torus (doughnut) sliced by a plane perpendicular to its axis, a paraboloid. These are some examples.
The cross section of a paraboloid, when sliced parallel to its axis of symmetry, is a parabola. If the slice is made perpendicular to the axis, the cross section can be a circle or an ellipse, depending on the orientation and position of the cut. The specific shape of the cross section will vary based on the location and angle of the slice in relation to the paraboloid.
Sphere
The vertical cross section of a square pyramid is a triangle. When the pyramid is sliced vertically through its apex and down to the base, the resulting shape is a triangular profile that includes the apex at the top and the edges of the base at the bottom. The height of the triangle corresponds to the height of the pyramid, while the base of the triangle spans the width of the base of the pyramid.
They would be two right triangular pyramids.
A sphere, a cone, a section of a sphere or ellipsoid, a torus (doughnut) sliced by a plane perpendicular to its axis, a paraboloid. These are some examples.
The cross section of a paraboloid, when sliced parallel to its axis of symmetry, is a parabola. If the slice is made perpendicular to the axis, the cross section can be a circle or an ellipse, depending on the orientation and position of the cut. The specific shape of the cross section will vary based on the location and angle of the slice in relation to the paraboloid.
There are many possible answers: A sphere sliced by a plane. An ellipsoid with two equal radii, sliced by a plane parallel to them. A paraboloid sliced by a plane perpendicular to its axis. A cone.
When a pyramid is sliced at an angle, the shape formed depends on the angle and position of the cut. If the slice is made parallel to the base, a smaller, similar pyramid is created. If the cut is made at an angle that is not parallel to the base, the resulting shape is typically a trapezoid or a polygon, depending on the specific geometry of the slice and the original pyramid.
It depends on the rock. Pumice is very weak and can be sliced through easily. Sandstone may be sliced through depending on its strength. Generally most rock types on the planet are are too hard to be sliced through with a sword.
The shape of the cross section depends on the 3D object being sliced. For example, if you slice through a cylinder horizontally, the cross section would be a circle. If you cut through a cube diagonally, the cross section could be a triangle or a rectangle, depending on the angle of the cut. Thus, the specific 2D shape observed in the cross section varies based on the object's geometry and the orientation of the cut.
A cone, or a parabolic section, or a section of a sphere like a hemisphere, or a torus (donut) sliced in half sideways.
The shape of a pyramid without its top is called a frustum. A frustum is formed when a pyramid is sliced parallel to its base, resulting in a truncated shape that has two parallel bases: one larger and one smaller. This geometric figure retains the original triangular faces of the pyramid, minus the apex.
The cross-section of a cube can vary depending on how it is cut. If sliced parallel to one of its faces, the cross-section will be a square. If cut diagonally, the cross-section can be a rectangle or a more complex polygon, depending on the angle and position of the cut.