Q: What two dimensional shape could not be the result of taking a cross section of a rectangular pyramid?

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It depends on the pyramid. If it is a square based pyramid, a horizontal plane will give a square cross section, a plane inclined by a rotation parallel to one of the base axes will give a rectangular cross section whereas a plane inclined by rotation along both basal axes will result in a parallelogram cross section. Not sure how you get a parallelogram from a pentagonal or hexagonal (etc) pyramid.

A pyramid can have a polygon with any number of sides as its base. A triangular pyramid (tetrahedron, the Platonic solid) and the rectangular based pyramid (like the Egyptian ones) are better known, but that is simply a result of poor imagination. If a pyramid has an n-gon as its base then it will have: 2 * n edges n + 1 faces and n + 1 vertices.

I am not sure how it was originally obtained. In some math book I saw how a specific triangular prism could be divided into three congruent pyramids.The formulat for the volume of a pyramid, or of a cone for that matter, can be obtained quite easily with calculus. The basic idea is to divide the pyramid into thin slices, and calculate the area of each (assuming that each slice is a rectangular block). You might do an approximation in Excel. The thinner the individual slices, the more accurate the result. (Calculus uses more advanced methods, to get the result quicker.)I am not sure how it was originally obtained. In some math book I saw how a specific triangular prism could be divided into three congruent pyramids.The formulat for the volume of a pyramid, or of a cone for that matter, can be obtained quite easily with calculus. The basic idea is to divide the pyramid into thin slices, and calculate the area of each (assuming that each slice is a rectangular block). You might do an approximation in Excel. The thinner the individual slices, the more accurate the result. (Calculus uses more advanced methods, to get the result quicker.)I am not sure how it was originally obtained. In some math book I saw how a specific triangular prism could be divided into three congruent pyramids.The formulat for the volume of a pyramid, or of a cone for that matter, can be obtained quite easily with calculus. The basic idea is to divide the pyramid into thin slices, and calculate the area of each (assuming that each slice is a rectangular block). You might do an approximation in Excel. The thinner the individual slices, the more accurate the result. (Calculus uses more advanced methods, to get the result quicker.)I am not sure how it was originally obtained. In some math book I saw how a specific triangular prism could be divided into three congruent pyramids.The formulat for the volume of a pyramid, or of a cone for that matter, can be obtained quite easily with calculus. The basic idea is to divide the pyramid into thin slices, and calculate the area of each (assuming that each slice is a rectangular block). You might do an approximation in Excel. The thinner the individual slices, the more accurate the result. (Calculus uses more advanced methods, to get the result quicker.)

I guess the result could be any 2d shape, depending on the 3d shape you slice.

It creates a triangular frustum.

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It depends on the pyramid. If it is a square based pyramid, a horizontal plane will give a square cross section, a plane inclined by a rotation parallel to one of the base axes will give a rectangular cross section whereas a plane inclined by rotation along both basal axes will result in a parallelogram cross section. Not sure how you get a parallelogram from a pentagonal or hexagonal (etc) pyramid.

A pyramid can have a polygon with any number of sides as its base. A triangular pyramid (tetrahedron, the Platonic solid) and the rectangular based pyramid (like the Egyptian ones) are better known, but that is simply a result of poor imagination. If a pyramid has an n-gon as its base then it will have: 2 * n edges n + 1 faces and n + 1 vertices.

I am not sure how it was originally obtained. In some math book I saw how a specific triangular prism could be divided into three congruent pyramids.The formulat for the volume of a pyramid, or of a cone for that matter, can be obtained quite easily with calculus. The basic idea is to divide the pyramid into thin slices, and calculate the area of each (assuming that each slice is a rectangular block). You might do an approximation in Excel. The thinner the individual slices, the more accurate the result. (Calculus uses more advanced methods, to get the result quicker.)I am not sure how it was originally obtained. In some math book I saw how a specific triangular prism could be divided into three congruent pyramids.The formulat for the volume of a pyramid, or of a cone for that matter, can be obtained quite easily with calculus. The basic idea is to divide the pyramid into thin slices, and calculate the area of each (assuming that each slice is a rectangular block). You might do an approximation in Excel. The thinner the individual slices, the more accurate the result. (Calculus uses more advanced methods, to get the result quicker.)I am not sure how it was originally obtained. In some math book I saw how a specific triangular prism could be divided into three congruent pyramids.The formulat for the volume of a pyramid, or of a cone for that matter, can be obtained quite easily with calculus. The basic idea is to divide the pyramid into thin slices, and calculate the area of each (assuming that each slice is a rectangular block). You might do an approximation in Excel. The thinner the individual slices, the more accurate the result. (Calculus uses more advanced methods, to get the result quicker.)I am not sure how it was originally obtained. In some math book I saw how a specific triangular prism could be divided into three congruent pyramids.The formulat for the volume of a pyramid, or of a cone for that matter, can be obtained quite easily with calculus. The basic idea is to divide the pyramid into thin slices, and calculate the area of each (assuming that each slice is a rectangular block). You might do an approximation in Excel. The thinner the individual slices, the more accurate the result. (Calculus uses more advanced methods, to get the result quicker.)

I guess the result could be any 2d shape, depending on the 3d shape you slice.

According to the question the mass appears to occupy 1-dimensional space which is not possible. As a result it is not possible to answer the question.According to the question the mass appears to occupy 1-dimensional space which is not possible. As a result it is not possible to answer the question.According to the question the mass appears to occupy 1-dimensional space which is not possible. As a result it is not possible to answer the question.According to the question the mass appears to occupy 1-dimensional space which is not possible. As a result it is not possible to answer the question.

summer 2009 result of AMIE section B will be declared on 15th Sep-09

It creates a triangular frustum.

Rectangular prisms are shapes which are easy to stack. As a result. many goods are transported in the form of rectangular prisms, or shapes approximating them: eg six packs of cans, ream of printer paper, bundle of newspapers. Furthermore, they are bundled together on palettes, into shipping containers, etc which are also rectangular prisms.

the purpose of frozen section is to let the tissue become hardness. because the frozen section used for immediately result

Paintings no longer looked so flat or two dimensional. Perspective allowed for the illusion of space and three dimensions in a two dimensional form.

Personally I find that pyramids are best observed alone, not in groups.

None. A polygon is a 2-dimensional shape. It cannot be multiplied by anything such that the result is a number.