Aim: How do you find the surface area and volume of a sphere?
April 18, 2012


Spheres: A Sphere is the set of all points in space equidistant from a given point called the center.

Volume:                                                                                       Surface Area:

                                      



Surface Area:

Aim: How do we find the volume of pyramids and cones?
April 17, 2012

Volume of a Pyramid

A pyramid has a base and triangular sides which rise to meet at the same point. The base may be any polygon such as a square, rectangle, triangle, etc. The general formula for the volume of a pyramid is:

Area of the base * Height * 1/3

The volume of a pyramid with a rectangular base is equal to: 

Length_of_base * Width_of_base * Height * 1/3

                                           

Volume of a Cone

The volume of a cone is 1/3(Area of Base)(height) = 1/3 π r² h

                                          

Aim: How do we find surface area and lateral area of prisms and cylinders?

A faster way to find lateral area:

L.A = ph

Surface area = lateral area + area of the bases
 ( S.A = L.A + 2B)

The surface area of a prism = 2 × area of base  +  perimeter of base × H

The actual formula used to find the surface area will depend on the shape of the base of the prism.

Aim: How do we identify polygons?
April 02, 2012




 Solid Geometry
Solid geometry is the geometry of the 3-dimensional space.
It is called three-dimensional, or 3D because there are three dimensions width, depth and height.

Properties:
Solids have properties, such as
- volume
- surface area

There are two main types of solids, "polyhedra" and "non-polyhedra"

Polyhedra- They must have have flat faces
 - prisms , pyramids , and platonic solids

Non-polyhedra- if any surface is not flat.
- sphere , cylinder and cone

Prisms: A prism has the same cross section all along its path/length.

Cross sections : A cross section is the shape you get when cutting straight across an object.

A prism is a solid with bases that are 2 congruent polygons. The other sides of the prism are called the lateral faces.

A prism is named by the shape of its base.

Aim: How do we find the area of a circle?

Circle area conjecture: The area of a circle is given by the formula, Area = πr² , where A is the area, r is the radius of the circle.

       Example:

 

Aim:How do we find the area of regular polygons?
March 19, 2012


The area of a regular polygon:
   You can divide a regular polygon into congruent isosceles triangles by drawing segments to each vertex.

Base: S (side)        Altitude: A (apothem)

The variable A appears in the formula for regular polygons. It stands for the length called the apothem, the perpendicular segment from the center to the side of the polygon.


Regular polygon area conjecture:
    The area of a regular polygon is given by the formula 1/2nas, where A is the area, a is the apothem, n is the number of sides ans S is the length.

                   formula: 1/2nas or p= 1/2Pa

Aim:How do we find the area of parallelograms, kites and trapezoids?

Area of parallelograms: 
       Area=base x height
                       

Area of trapezoids:
        Area=1/2 x height (b1 + b2)


                                      




















Area of kite: 2 pairs of consecutive congruent sides.
               Area= d1 + d2/2