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Q: What solid has cross sections parallel to the base?

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It is a horizontal cross-section. Its shape will depend on the shape of the solid and its orientation.

there are no square pyramids. they are not of the same

The vertical cross sections are trapezia or triangles. The horizontal cross sections are rectangles which are mathematically similar to the base.

A cylinder has a circular cross section that is parallel to its base.

It depends which orientation the cube has to the cake and which shape the cake is. However, assuming you meant a cube shaped cake was cut parallel to its base: It will be a cuboid.

Related questions

All cross sections of a square pyramid that are parallel to the base are squares

Circle: If the knife is perpendicular to the axis of the cone.Ellipse: If the knife is between (perpendicular to the axis of the cone) and (parallel to the side of the cone).Parabola: If the knife is between (parallel to the side of the cone) and (parallel to the axis of the cone).Hyperbola: If the knife is parallel to the axis of the cone.Triangle: If the knife is perpendicular to the base of the cone.Point: If the knife is parallel to the base the cone and through the apex

It is a horizontal cross-section. Its shape will depend on the shape of the solid and its orientation.

there are no square pyramids. they are not of the same

Sphere

A tapered prism.

The vertical cross sections are trapezia or triangles. The horizontal cross sections are rectangles which are mathematically similar to the base.

A cylinder has a circular cross section that is parallel to its base.

The answer would be a right cylinder. A right cylinder is a cylinder that has a closed circular surface having two parallel bases on both the ends and whose elements are perpendicular to its base.

(The cone I am referring to in the comparison below to a pyramid is not the mathematical cone, but a truncated half cone)Both cone and pyramid have a bottom surface (base) and a heightBoth have a volume of 1/3 the area of the base times the heightBoth have cross sections parallel to the base that are congruent to each other (all parallel sections are congruent to each other)Both have a "point" where the the area of the cross section vanishes to 0

It depends which orientation the cube has to the cake and which shape the cake is. However, assuming you meant a cube shaped cake was cut parallel to its base: It will be a cuboid.

because the cylinder has a circular base and a triangular prism has a triangular base so they are both basic shapes.

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