Aim : How do you find the surface area and volume of a sphere ?

Definition of a Sphere -
a sphere is the set of all points in space equidistant from a given point called the center .

Formula for the Surface Area of a Sphere :
SA= 4 pi r squared

Formula for the Volume of a Sphere :
V= 4/3 n r cubed

Aim : How do we find the volume of pyramids and cones ?

Formula for Volume of a Pyramid :
V= 1/3Bh ( where B is the area of the base )

Formula for the Volume of a Cone :
V= 1/3Bh ( where B is the area of the base )

Aim : How do we find the surface area and lateral area of pyramids and cones ?

A pyramid is a solid that connects a polygon base to a point.

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

Formula for Surface Area of a Prism :
 LxWx2 + LxHx2 + WxHx2
( L meaning length ; W meaning Width ; H meaning Height )

Formula for Surface Area of a Cylinder :
2(pi r squared) + (2 pi r) H

Aim : How do we identify solids ?

Solid Geometry is the geometry of 3-dimensional space.
involves width , height and length.
Volume( think how much water can fit! )
Surface Area  ( space around it )

Two Main Types .

Polyhedra - must have flat faces, polygons.
includes- prisms , platonics , pyramids etc .

Non Polyhedra - any surface with no flat surface
includes- spheres , cylinders , torus , cones .

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

A is the area and R is the radius  .
Area is  - A =pieRsquared

Aim: How do we calculate the area of rectangles and triangles ?

Triangle Area Conjecture - the area of a triangle is given by the formula , where A is the area , B is the length of the base and H is the height of a triangle.

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

Formula for the Area of a Parrallelogram:
A= b x h

Example: A= b x h
                A= 12cm x 9cm
                A= 108cm

Formula for the Area of a Kite:
A= d1d2(1/2)

Example: A=d1d2(1/2)
                A= 6 x 10 x (1/2)
                A= 30

Formula for the Area of a Trapezoid:
A= (b1+b2) x h 
          2

Aim : How do we find the locus of points ?

Locus is set of all points that satify a given condition .

1) Equidistant - a circle with the original point at its center.
2)A line the middle of two points.
3)Two parallel lines on the opposite sides of the original line.
4)A line through the middle of two lines.
5)Two intersecting lines half way between two original lines.

Aim : How do we solve logic problems using conditionals ?
 
Converse is just switching the hypothesis and the conclusion .
When the conditional and the converse are both true its bi conditional.
For Example , if this month is August , then next month is September .
Contrapositive
Contra meaning "against" or "opposite".

Aim: What is a mathematical statement ?

A mathematical statement is a statement that can be judged to be true false .

Aim: How do you graph dilations ?

Dilation is a form of transformation that causes a image to stretch or shrink in proportion to its original size .

For example . .

   Find the image of (3,-2) under dilation osf D2 ?
                                x 2
                               ( 6,-4 ) = New Image

Aim: How can we graph transformations that are reflections ?

 It's way easy to find Reflection .
x axis -> (x,y) -> (x,-y)
y axis -> (x,y) -> (-x,y) .