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# 3D Geometry

### 1-14-14

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1.It is called three-dimensional, or3D because there are three dimensions: width, depth andheight.

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2. A polyhedron is a solid with flat faces

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3. non-polyhedron-

3 dimensional figures that havecurved surfaces

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4. A prism has flat sides and the same cross section all along its length !

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5. This tells you where the top (apex) of the pyramid is. If the apex is directly above the center of the base, then it is a Right Pyramid, otherwise it is an Oblique Pyramid.

This tells us about the shape of the base. If the base is a regular polygon, then it is a Regular Pyramid, otherwise it is an Irregular Pyramid.

The Volume of a Pyramid

• 1/3 × [Base Area] × Height

The Surface Area of a Pyramid

When all side faces are the same:

• [Base Area] + 1/2 × Perimeter × [Slant Length]

When side faces are different:

• [Base Area]+[Lateral Area]

Notes On Surface Area

The Surface Area has two parts: the area of the base (the Base Area), and the area of the side faces (the Lateral Area).

For Base Area :

It depends on the shape, there are different formulas for triangle, square, etc. See Areafor formulas, or our Area Calculation Tool

For Lateral Area :

When all the side faces are the same:

• Just multiply the perimeter by the "slant length" and divide by 2. This is because the side faces are always triangles and the triangle formula is "base times height divided by 2"

But if the side faces are different (such as an "irregular" pyramid) then add up the area of each triangular shape to find the total lateral area.

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6. Cone-

A solid (3-dimensional) object that has a circular base and one vertex

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7. A solid object with:

* two identical flat ends that are circular or elliptical

* and one curved side.

It has the same cross-section from one end to the other.

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8. Sphere-

It is perfectly symmetrical It has no edges or vertices (corners) It is not a polyhedron All points on the surface are the same distance from the center.

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9. Torus-

It can be made by revolving a small circle along a line made by another circle. It has no edges or vertices It is not a polyhedron

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10. Net-

A pattern that you can cut and fold to make a model of a solid shape.

This is a net of a cube.

Also means what is left after all deductions have been made..

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