1 / 12

# Lesson 9 - PowerPoint PPT Presentation

Lesson 9. Three-Dimensional Geometry. Planes. A plane is a flat surface (think tabletop) that extends forever in all directions. It is a two-dimensional figure. Three non-collinear points determine a plane. So far, all of the geometry we’ve done in these lessons took place in a plane.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about 'Lesson 9' - tejana

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### Lesson 9

Three-Dimensional Geometry

• A plane is a flat surface (think tabletop) that extends forever in all directions.

• It is a two-dimensional figure.

• Three non-collinear points determine a plane.

• So far, all of the geometry we’ve done in these lessons took place in a plane.

• But objects in the real world are three-dimensional, so we will have to leave the plane and talk about objects like spheres, boxes, cones, and cylinders.

W

L

Boxes

• A box (also called a right parallelepiped) is just what the name box suggests. One is shown to the right.

• A box has six rectangular faces, twelve edges, and eight vertices.

• A box has a length, width, and height (or base, height, and depth).

• These three dimensions are marked in the figure.

• The volume of a three-dimensional object measures the amount of “space” the object takes up.

• Volume can be thought of as a capacity and units for volume include cubic centimeters cubic yards, and gallons.

• The surface area of a three-dimensional object is, as the name suggests, the area of its surface.

W

L

Volume and Surface Area of a Box

• The volume of a box is found by multiplying its three dimensions together:

• The surface area of a box is found by adding the areas of its six rectangular faces. Since we already know how to find the area of a rectangle, no formula is necessary.

5

8

Example

• Find the volume and surface area of the box shown.

• The volume is

• The surface area is

• A cube is a box with three equal dimensions (length = width = height).

• Since a cube is a box, the same formulas for volume and surface area hold.

• If s denotes the length of an edge of a cube, then its volume is and its surface area is

• A prism is a three-dimensional solid with two congruent bases that lie in parallel planes, one directly above the other, and with edges connecting the corresponding vertices of the bases.

• The bases can be any shape and the name of the prism is based on the name of the bases.

• For example, the prism shown at right is a triangular prism.

• The volume of a prism is found by multiplying the area of its base by its height.

• The surface area of a prism is found by adding the areas of all of its polygonal faces including its bases.

r

Cylinders

• A cylinder is a prism in which the bases are circles.

• The volume of a cylinder is the area of its base times its height:

• The surface area of a cylinder is:

• A pyramid is a three-dimensional solid with one polygonal base and with line segments connecting the vertices of the base to a single point somewhere above the base.

• There are different kinds of pyramids depending on what shape the base is. To the right is a rectangular pyramid.

• To find the volume of a pyramid, multiply one-third the area of its base by its height.

• To find the surface area of a pyramid, add the areas of all of its faces.

r

Cones

• A cone is like a pyramid but with a circular base instead of a polygonal base.

• The volume of a cone is one-third the area of its base times its height:

• The surface area of a cone is:

Spheres

• Sphere is the mathematical word for “ball.” It is the set of all points in space a fixed distance from a given point called the center of the sphere.

• A sphere has a radius and diameter, just like a circle does.

• The volume of a sphere is:

• The surface area of a sphere is: