# 3D Geometry

### 1-14-14

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1.It is called **three-dimensional**, or**3D** because there are three dimensions: *width, depth *and*height.*

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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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