3woooli

==[|×]==

__Surface Area and Volume.__
-Develop the concepts and maximizing volume and minimizing surface area.
 * Objectives of the section:**

-Surface area of a regular prism=2Lw+2wh
 * Suface area ad volume formulas:**

-Volume of a regular prism=Lwh

-Suface area of a cube=6s²

-Volume of a cube=s³


 * example problems:**

-What is the surface area of the cube if the hieght is 11, the length is 11 and the width is 1?

-What is the volume of a regular prism if the hieght is 4, the length is 32 and the width is 3?

-What is the Volume of a cube is the hieght if 192, the length is 192 and the width is 192?

-What is the surface area of the regular prism if the hieght is 32, the length is 35 and the width is 172? prism

-Define and use a fomula for finding the surface area of a right pism.
 * Objectives of the section:**

-Define and use a formula for finding the volume of a right prism.

-Use Cavalieris principle to develop a formula for the volume of a right of oblique prism.

-Altitude - a segment in a prism that has a endpoints in a planes
 * Defined words:**

-Height - length of the altitude

-Surface area of a right prism = Lateral area + 2×Base area
 * Formulas:**

-Volume of a prism = Base area ×Height

-If two solids hace equal heights and the cross sections fformed by every plane parallel to the bases of both solids have equal areas, then the two solids have equal volumes.
 * Cavalieris Principle:**

-**find the surface area and the volume of the right triangular prism if the altitude is 2, line FC is 30, line DE is 10, line EF is 21, and line FD is 19
 * Example problems:





-Define and use a formula for th surface area of a regular pyramid
 * Objectives of the section:**

-Define and use a formula for the volume of the pyramid

-Pyramid: is a polyhedron consisting of a base, which is a polygon, and three or more lateral faces
 * Defined words:**

-Vertex: where the three or more lateral faces all meet

-Base edge: each lateral faces has one edge in common with the base

-Lateral edge: the intersection of two lateral faces is a lateral edge

-Triangular pyramid: has a triangle base, and has 3 lateral faces
 * Types of pyramids:**

-Rectangular pyramid: Has a rectagle base, and has 4 lateral faces

-Pentagonal pyramid: has a pentagon base, and has 5 lateral faces

-hexagonal pyramid, has a hexagon base, and 6 later faces

- Surface area of a pyramid= Lateral area+ Base area
 * Formulas:**

-Volume of a pyramid= 1/3×Base×height

- Draw a net for a pentagonal pyramid
 * Example problems:**

- Draw a net for a hexagonal pyramid

- Draw a net for a rectangular pyramid

- Find the surface area of a triangular pyramid if the lateral faces are isometric and the length is 32

- Find the surface area of a hexagonal pyramid if the lateral faces are isometric and the length is 62

- Find the surface area of a pentagonal pyramid if the lateral faces are isometric and the length is 43



-Define and use a formula for the surface area of a right cylinder.
 * Objectives of the section:**

-Define and use a formula for the volume of a cylinder.

-Cylinder: is a solid that consists of a circular region and its translated image on a parallel plane, with a lateralsurface connecting the circles.
 * Defined words:**

-Axis: is the segment joining the centers of two bases

-Oblique cylinder: id the axis isnt parellel to the altitude

-Right cylinder: if the axis is parellel to the altitude

-Surface area of a right cylinder= Lateral area + 2× Base area
 * Formulas:**

-Volume of cylinder= Base area × Height or 3.14 × radius² × height

-What is the Volume of the cylinder is the height is 30 and the radius is 51
 * Example problems:**

-What is the Surface area or the cylinder if the height is 21 and the redius is 2

-What is the Volume of the cylinder is the height is 1 and the radius is 74

-What is the surface area of the cylinder is the height is 46 and the radius is 3



-Define and use the formula for the surface area of a cone
 * Objectives of the section:**

-Define and use the formula for the volume of a cone

-Cone: a three dimensional figure that that has a circle for a base point with one point called a vertex
 * Defined words:**

-Oblique cone: the altitude isnt perpendicular to the center of the base

-Right cone: the altitude is purpendicular to the center of the base

-Surface area of a right cone= Lateral area+Base area or 3.14×Radius×Slant height+3.14×Radius
 * Formulas:**

-Volume of a cone= 1/3×Base area×Height

-Find the surface area of the right cone if the radius is 3, the slant hieght is 5, and the height is 4
 * Example problems:**

-Find the volume of a cone if the height is45, and the radius is 7

-Find the volume of the cone is the height is 34 and the radius is 56

-Find the surface area of the right cone is the radius is 6, the height slant is 10 and the height is 8



-Define and use the formula for the surface area of a sphere
 * Objectives of the section:**

-Define and use the formula for the volume of a sphere

-Sphere: is a symmetrical geometrical object. Considered a perfectly round ball or the earth.
 * Defined words:**

-Volume of a sphere= 4/3×3.14×Radius³
 * Formulas:**

-Surface area of a sphere= 4×3.14×Radius²

-find the volume of the sphere is the radius is: -23 -334 -342 -6 -75 -45
 * Example problems:**



-Define various transformations in three dimensional space -Solve problems by using transformations in three dimensional space
 * Objectives of the section:**

formulas for volume and suface area of shapes:http://www.math.com/tables/geometry/volumes.ht [|formulas] for spheres [|all the formulas you need] [|Games]