nolale


 * __Link to Chapter 9 nolale33

Chapter 7.1 Surface area and Volume

Objectives:__**


 * Explore ratios of surface are to volume
 * develop the concepts of maximizing volume and minimizing surfacec area.

__Surface Area and Volume:__ The Surface area, S and volume, V of the right rectangular prism with length //l// width //w// and height //h// are S=2//lw+//2//wh+//2//lh// and V=//lwh// The surface area, S and the volume, V of a cube with the side s are S=6s^2 and V=s^3 Image from: http://id.mind.net/~za/mmts/geometrySection/surfaceAreasAndVolumes/box1.jpg

A cereal company is choosing between two box designs with the dimensions shown at right. Which design has the greater surface area and thus requires more material for the same volume? both boxes have a volume of 160 cubic inches. the surfaces area of box A is 2(8)(5)+2(4)(8)=184square inches The surface area of box B is 2(10)(8)+2(2)(10)=232 square inches. Box B has the greatest surface area!!!
 * __EXAMPLE__**:

__Related Sites Explaining Surface Area and Volume:__ Formulashttp://math2.org/math/geometry/areasvols.htm Math Examples Relating to Surface area. http://www.321know.com/geo79_x9.htm Math Examples Relating to Volume. http://www.321know.com/geo79_x7.htm

__**Surface area and Volume of prisms**__
 * __Chapter 7.2__**
 * __Objectives:__**


 * Define and use a formula for finding the surface area of a right prism
 * Define and use the formula for finding the volume of a right prism
 * Use Cavalieri's principle to develop a formula for the volume of a right or obique prism.

An **Altitude** of a prism is a segment that has endpoints in the panes containing the bases and that is perpedicular to both planes. The **hight** of a prism is the length of an altitude.

The Surface area S, of a right prism with lateral area L, base area B, perimeter p, and the height h is S=L+2B or S=hp+2B
 * Surface Area of Right prisms:**

The volume, V, of a prism with height h and base area B is V=Bh
 * Volume of a Prism**

EXAMPLE**:** An aquarium has the shape of a right regular hexagonal prism with the dementions shown at the right. Find the volume of the aquarium. Solution: The base of the aquarium has a perimeter of (14)(6), or 84 inches and an apothem of 7 squar root of 3 inches, so the base area is found as follows. B=1/2ap=1/2(84)(7 squar root of 3) =294/ 3= 509.22 squar inches The volume is V= Bh=(

http://argyll.epsb.ca/jreed/math9/strand3/3107.htm
 * Helpful Websites for Practice**


 * __Chapter 7.3__**
 * Surface area and volume of Pyramids**

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

A **pyramid** is a polyhedron consisting of a **base,** which is a polygon, and three or more **lateral faces**. The lateral faces are triangles that share a single vertex, called the **vertex of a pyramid**. Each lateral face has one edge in common with the base, called a **base edge**, The intersection of two lateral faces is a lateral **edge**. The **altitude** of a pyramid is the perpendicular segment from the vertex to the plane of the base. The **height** of the pyramid is the length of its altitude. A **regular pyramid** is a pyramid whose base is a regular polygon and whose lateral faces are congruent isosceles triangles. In a regular pyramid, all of the lateral edges are congruent, and the altitude intersects the base at it's center. The length of an altitude of a lateral face of a regular pyramid is called the slant height of the pyramid. Picture from: http://www.mathsisfun.com/geometry/images/triangular-pyramid-height.jpgt

The surface area, S, of 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=1/2Lp+B
 * Surface area of a Regular Pyramid:**

The volume V, of a pyramid with height h and base area B is V=1/3Bh.
 * Volume of a Pyramid:**

Surface area and Volume of a Cylinder:__**
 * __Chapter 7.4


 * __Objectives__**
 * Define and use a formula for the surface area if a right cylinder
 * Define and use a formula for the volume of a cylinder

A **Cylinder** is a solid that consist of a circular region and its translated image on a parallel plane, with a **lateral surface** connecting the circles. The faces formed by the circular region and its translated image are called the **bases** of the cylinder. An **altitude** of a cylinder is a segment that has endpoints in the planes congaing the bases and is perpendicular to both planes. The **height** of a cylinder is the length of a altitude. The axis of a cylinder is the segment joining the centers of the two bases If the **axis** of a cylinder is perpendicular to the bases, then the cylinder is a **right cylinder**. if not, it is an **oblique cylinder. Picture From:http://www.capesoft.com/docs/Draw/Metallic%20Cylinders.jpg ** __**Surface area of a Right Cylinder:**__ The surface area, S of a right cylinder with lateral area L, base area B, radius r, and height h is S= L+2B or S= 2( 3.14) RH + 2(3.14)R^2 __**Volume of Cylinder**__ The volume, V, of a cylinder with radius r, height h, and base area B is V=Bh or V =( 3.14) R^2h

__**Chapter 7.5 Surface Area and Volume of Cones.**__

__**Objectives:**__
 * Define and use the formula for the surface area of a cone.
 * Define and use the formula for the volume of a cone.

A **cone** is a three-dimensional figure that consists of a circular **base** and a curved **lateral surface** that connects the base to a single point not in the plane of the base, called the **vertex.** The **altitude** of a cone is the perpendicular segment from the vertex to the plane of the base. The **height** of the cone is the length of the altitude. If the altitude of a cone intersects the base of the cone at its center, the cone is a **right cone**. If not, it is an **oblique cone**.

__**Surface area of a Right Cone:**__ The surface area, S, of a right cone with lateral area L, base of area B, radius r, and slant height l is S=L+B or S= ( 3.14)RL+( 3.14)R^2

__**Volume of a cone**__ The volume, V, of a cone with radius r, height h, and base area B is V=1/3bh or V=1/3 ( 3.14)R^2h