dunant

=duan521 Chapter 9=

Geometry Wiki

7.1 Surface Area and Volume

1. Explore ratios of surface area to volume. 2. Develop the concepts of maximizing volume and minimizing surface area.
 * Objectives**


 * Surface Area and Volume Formulas:** The surface are, S, and volume, V, of a right rectangular prism with the length being l, width being w, and height being h are

S = 2lw + 2wh + 2lh and the volume formula: V + lwh.

The surface area,= S, and the volume of a cube with side s are

S = 6s squared and V = s cubed

Picture here: http://www.flickr.com/photos/rainbill/50768823/

7.2 Surface Area and Volume of Prisms

1. Define and use a formula for finding the surface area of a right prism. 2. Define and use a formula for finding the volume of a right prism. 3. Sue Cavalieri’s Principle to develop a formula for the volume of a right or oblique prism.
 * Objectives**

An **altitude** of a prism is a segment that has endpoints in the planes containing the bases and that is perpendicular to both planes. The **height** of any prism is the length of the altitude.

Picture-à http://www.flickr.com/photos/pulpolux/163672566/


 * Surface Area of a Right Prism:** The surface area, which is S, of a right prism with the lateral area L, base area being B, perimeter p, and the height being h is

S = L + 2B or S = hp + 2B.


 * Cavalieri’s Principle:** If, in 2 solids of an equal altitude, the sections made by planes parallel to and at the same distance from their respective bases are always equal, then the volumes of the 2 solids are equal.


 * Volume of a Prism:** The volume, which is V, of a prism with a heaight h, and base area B is

V = Bh

7.3 Surface Area and Volume of Pyramids

1. Define and use a formula for the surface area of a regular pyramid. 2. Define and use a formula for the volume of a pyramid.
 * Objectives**

a lateral edge.
 * Pyramid:** A polyhedron consisting of a base which is a polygon, and three or more lateral faces. The **lateral faces** that share a single vertex, this is called the vertex of the pyramid. Every lateral face has one edge in common with the base called a **base edge**. The intersection of 2 lateral faces is called

Picture http://www.flickr.com/photos/kevandotorg/75527387/

The **altitude** of a pyramid is the perpendicular segment from the vertex to the plane of the base. The **height** is the length of the altitude.

A **regular pyramid** is a pyramid that has a regular polygon as its base. The length of an altitude of a lateral face of a regular pyramid is called the **slant height** of the pyramid.


 * Surface Area of a Regular Pyramid:** The surface area which is S, if a regular pyramid with lateral area L, base area B, perimeter of the base p, and slant height l is

S = L + B or S = One half lp + B


 * Volume of a Pyramid:** The volume, V, of a pyramid with heaight h and base area B is

V = One third Bh

7.4 Surface Area and Volume of Cylinders

A **cylinder** is a solid that consists of a circular area and its translated image on a parallel plane, with a lateral surface connecting the circles.

Picture of cylinder http://www.flickr.com/photos/kalamakia/434722279/

The faces formed by the circular areas of a cylinder are known as the **bases** of the cylinder.

The **axis** of a cylinder is a segment joining the centers of the two bases.

If the axis of a cylinder is perpendicular to the 2 circular bases, then the cylinder is a **right cylinder**. If they are not perpendicular it is an **oblique cylinder.**


 * Surface Area of a Right Cylinder:** The surface area which is S, of a right cylinder with lateral area L, base area B, radius r, and height h is

S = L + 2B or S = 2Pirh + 2Pir squared

V = Bh or V = Pir squared h
 * Volume of a Cylinder:** The volume V, of a cylinder with radius r, height h, and base area B is

7.5 Surface Area and Volume of Cones

A cone is a 3D figure that consists of a circular base and a curved lateral surface that connects the base to a single point.

Picture http://www.flickr.com/photos/garythegit/292580805/

If the altitude of the cone intersects the base of the cone at its center, the cones a right cone. If it does not, it is oblique.


 * SA of a Right Cone:** The surface area S, of a right cone with lateral area L, base area B, radius r, and slant height l is

S = L + B or S = Pirl + Pir squared


 * Volume of a Cone:** The volume, V, of a cone with radius, r, height h, and base area B is

V = one third Bh or V = one third Pir squared h

Fun Geometry Links!

http://www.gamequarium.com/geometry.html

http://www.funbrain.com/poly/

http://www.aaaknow.com/geo.htm