sprbri

=spbr519--chp. 9 link= =__CHAPTER 7__=

OBJECTIVES:

 * Explore ratios of surface area to volume
 * Develop the concepts of maximizing volume ans minimizing surface area

VOCABULARY:

 * //None//

FORMULAS:

 * Surface Area of a Rectangular Prism
 * S=2lw+2wh+2lh (S-surface area, l-length, w-width, h-height)
 * Volume of a Rectangular Prism
 * V=lwh
 * Surface Area of a Cube
 * S=6s² (s-side)
 * Volume of a Cube
 * V=s³

Example: Anne is trying to put paper over the outside of her box for a school project but doesn't know how much paper to buy. She is covering all sides of the cube and the cube's side length is 6 inches long. How many inches of paper does Anne need?
 * answer at bottom*

OBJECTIVES:

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


 * Height of a Prism
 * The length of the altitude
 * Altitude of a Prism
 * A segment that has endpoints in the planes containing the bases and that is perpendicular to both planes.
 * Cavalieri's Principle
 * If 2 solids have equal heights and the cross sections formed by every plane parallel to the base of both solids have equal areas, then the two solids have equal volume.

FORMULAS:

 * Surface Area of a Right Prism
 * S=hp+2B (S-surface area, h-height, p-perimeter, B-base area)
 * Volume of a Prism
 * V=Bh (V-volume, B-base area, h-height)



Example: David is getting a new fish aquarium and wants to now how much water to fill it with. If the side lengths are 10 inches, 6 inches and 7 inches, what is the maximum volume of the tank?
 * answers at bottom*

OBJECTIVES

 * Define and use a formula for the surface area of a regular pyramid
 * Define and use a formula for the volume of a pyramid

VOCABULARY:

 * Pyramid
 * A polyhedron consisting of a base, which is a polygon, and 3 or more lateral faces.
 * Base
 * The polygonal face that is opposite the vertex.
 * Lateral Faces
 * The faces of a prism or pyramid that are not bases.
 * Vertex of a Pyramid
 * A point where the edges of a figure intersect.
 * Base Edge
 * An edge that is part of the base of a pyramid; Each lateral face has one edge in common.
 * Lateral Edge
 * The intersection of 2 lateral faces.
 * Altitude of a Pyramid
 * A segment from the vertex perpendicular to the plane base.
 * Height
 * The length of the altitude.
 * Regular Pyramid
 * A pyramid whose base is a regular polygon and whose lateral faces are congruent.
 * Slant Height
 * In a regular pyramid, the length of the altitude of a lateral face.

FORMULAS:
Example: Greta and her family is taking a vacation to the pyramids of Egypt. Greta wants to figure out how much space the pyramid takes up. If the base area is 100 square feet and the height is 50 feet, then what is the volume of the pyramid?
 * Surface Area of a Regular Pyramid
 * S=½lp+B (S-surface area, l-slant height, p-perimeter of base, B-base area)
 * Volume of a Pyramid
 * V=1/3Bh (V-volume, B-base area, h-height)
 * answers on bottom*

OBJECTIVES:

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

VOCABULARY:

 * Cylinder
 * A solid that consists of a circular region and it's translated image in a parallel plane with a lateral surface connecting the circles
 * Lateral Surface
 * The curved surface of a cylinder.
 * Base
 * The circular faces of the cylinder.
 * Altitude
 * A segment that has endpoints in the planes connecting the bases and is perpendicular to both planes.
 * Height
 * The length of the altitude.
 * Axis
 * The segment joining the centers of the 2 bases.
 * Right Cylinder
 * A cylinder whose axis is perpendicular to the bases.
 * Oblique Cylinder
 * A cylinder that isn't a right cylinder.

FORMULAS:

 * Surface Area of a Right Cylinder
 * S=2(pi)rh+2(pi)r² (pi-3.14, r-radius, h-height)
 * Volume of a Cylinder
 * V=(pi)r²h



Example: Tommy wants to know how much soup is in his tomato soup can. If the can is 4 inches tall and the radius of the can's base is 1.5 inches, approxamently how much soup is in Tommy's can?
 * answers at bottom*

OBJECTIVES:

 * Define and use the formula for the surface area of a cone
 * Define and use the formula for the volume of a cone

VOCABULARY:

 * Cone
 * A 3-D 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.
 * Base
 * The circular face of a cone.
 * Lateral Surface
 * The curved surface of a cone.
 * Vertex
 * The point opposite the base of the cone.
 * Altitude
 * A segment from the vertex perpendicular to the plane of the base.
 * Height
 * The length of the altitude.
 * Right Cone
 * A cone in which the altitude intersects the base at it's center point
 * Oblique cone
 * A cone that is not a right cone.

FORMULAS:

 * Surface Area of a Right Cone
 * S=(pi)rl+(pi)r² (pi-3.14, l-slant height)
 * Volume of a Cone
 * V=1/3(pi)r²h

Example: Suzy wants to know how much ice cream can be held inside the cone. The diameter of the bace in 4 inches and the height is 8 inches. How much ice cream can Suzy's cone hold?
 * answers at bottom*

OBJECTIVES:

 * Define and use the formula for the surface area of a sphere
 * Define and use the formula for the volume of a sphere

VOCABULARY:

 * Sphere
 * The set of points in space that are equidistant from a given point known as the center of the sphere.
 * Annulus
 * The region between 2 circles in a plane that have the same center but different radii.

FORMULAS:
Example: Jack wants to know how much fabric will fit over a styrofoam sphere in order to create the Earth for a science project. If the styrofoam sphere has a diameter of 30 centimeters, then how much fabric will Jack need?
 * Surface Area of a Sphere
 * S=4(pi)r² (pi-3.14, r-radius)
 * Volume of a Sphere
 * V=4/3(pi)r³
 * answers at bottom*

ANSWERS:
SECTION 1: 36 inches³ SECTION 2: 420 inches³ SECTION 3: 1666.7 feet³ SECTION 4: 28.3 inches³ SECTION 5: 134.04 inches³ SECTION 6: 2827.43 centimeters²

MORE EXAMPLES:
1-If you have a right triangular prism with a heigth of 10 inches and a triangular base edges of 5 inches and 8 inches, what is the volume? V=Bh V=(½bh)h V=[½(5)(8)]10 V=(20)10 V=30 inches³

OTHER HELPFUL SITES:
[|Click here] and scroll down to either Surface Area or Volume to find further help. [|Click here] for additional help and also a few games. [|Click here] for additional help. Look at the section that is labled three-dimensional figures and click on the section you need help in. [|Click here] to view videos that take you step by step through surface area and volume. Click on Surface Area and Volume under the Video (Flash) Lessons section.