3whisam

= = =1 . Surface Area and Volume=



Surface Area & Volume for a [|cube2] [|Examples] of Volume. [|Help] with surface area of a cube.

- Develope the concepts of maximizing volume and minimizing surface area.
 * Objectives** :

S = Surface Area V = Volume L = Length W = Width H = Height
 * Surface Area And Volume -**

and V = lwh
 * Formulas** : S = 2lw + 2wh + 2lh

=2 . Surface Area and Volume of Prism -=



- Define and use a formula for finding the surface area of a right prism. - Use Cavaliari's Principle to develop a formula for the volume of a right or oblique prism.
 * Objectives** :
 * -** Define and use a formula for finding the volume of a right prism.


 * Vocabulary** :
 * Altitude** of a prism is a segment tat has endpoints in the planes that contain the bases and that is perpendicular to both planes.
 * Height** - The length of the altitude of the prism.

__Surface Area of a Right Prism__ - Surface Area - //S//, of a right prism with lateral area //L,// base area - //B//, perimeter - //p//, and height - //h// is S = L + 2B __or__ S = hp + 2B
 * Boxes** :

__Calalier's Princple__ - If the two solids have = heights and the cross sections formed by every plane parallel to the bases of both solids have = areas, then the two solids have two = volumes

__Volume of a Prism__ - V = Bh

=3 . Surface Area and Volume of Pyramids -=

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

The lateral faces would be triangles that share a single vertex, called the **vertex of the pyramid**. Each lateral face has 1 edge in common with the base, called a **base edge**. The intersection of 2 lateral faces is called a **lateral edge**.
 * Vocabulary** :
 * Pyramid** is a polyhedron containing of a **base** which is a polygon, & 3 or more **lateral** **faces**.
 * Altitude** - is the perpendicular segment from the vertex to the plane of the base.
 * Height** - It is the length of the altitude.
 * Regular pyramid** - a pyramid thats base is a regular polygon and that the lateral faces are congruent isosceles triangles. All the lateral edges are congruent and the altitude intersects at the base in the center.
 * Slant height** - The length of an altitude of a lateral face of a regular pyramid.

//Surface area of a regular pyramid// - S = Surface Area L = Lateral Area B = Base P = Perimeter //l// = slant height __Formula__ - S = L + B **or** S = 1/2//l//p + B
 * Boxes** :

//Volume of a pyramid -// V = Volume H = Height B = Base __Formula__ - V = 1/3Bh

=4 . Surface Area and Volume of Cylinders -=



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

//Surface Area of a right cylinder// - Surface Area - S Lateral Area - L Base Area - B Radius - //r// Height - //h// __Formula__ : S = L + 2B or //S = 2// π//rh// + 2 π//r//²
 * Vocabulary** -
 * Cylinder** - a solid that consists of a circular region and it is translated image on a parallel plane.
 * Lateral surface** - connects the circles.
 * Bases** - The faces formed by the circular region and its translated image.
 * Altitude** - the segment that has endpoints in the planes containing the bases and is perpendicular to both planes.
 * Height** - the length of an altitude.
 * Axis** - the segment joining the centers of the two bases.
 * Right** **cylinder** - the cylinder is perpendicular to the bases.
 * Oblique** **cylinder** - the cylinder is not perpendicular to the bases.
 * Boxes** -

//Volume of a Cylinder// - Volume - V Radius - r Height - h Base - B __Formula__ : V = Bh or V = πr²h

=5 . Surface Area and Volume of Cones -=

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

__Cone__ - a three-dimensional figure. __Base__ - a circular bottom __Lateral__ __surface__ - curved around __Vertex__ - connects the base to a single point not in a the plane of the base. __Altitude__ - perpendicular segment from the vertex to the plane base. __Height__ - length of the altitude. __Right__ __cone__ - intersects the base of the cone at it's center. __Oblique__ __cone__ - does not intersect at the base of the cone in the center, it is not right.
 * Vocabulary** :

//__Surface area of a right cone__ -// Surface Area - S Lateral Area - L Base - B Radius - r Slant Height - //l
 * Boxes** :

Formulas :// S = L + B or S = πr//l +// π//r//²

__//Volume of a Cone//__ - Volume - V Radius - r Height - h Base - B

//Formula// : V = 1/3Bh or V = 1/3πr²h

=6 . Surface Area and Volume of Spheres -=

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

//Sphere// - the set of all points in space that are the same distance from a given point known as the center of the sphere.
 * Vocabulary** :

//Volume of a Sphere -// V = 4/3πr³ //Surface Area of a sphere -// S = 4πr²
 * Boxes** :

=7 . Three-Dimensional Symmetry -=



Do you know your [|symmetry] ?

- Define various transformations in three-dimensional space. - Solve problems by using transformations in three-dimensional space.
 * Objectives** :