Arc length and Circumference Class Notes
In a polygon, we measure the perimeter. In a circle, ellipse, or other closed curve, we
measure the circumference.
In a circle with circumference C, diameter d, and radius r, then C d or C 2 r .
The ratio of circum
Multiplication, Area, and Volume
Rectangles can be used to model multiplication of binomials:
EX 1: What binomial multiplication is pictured? Perform the multiplication.
5x
1
3x
2
Binomials: _
Answer: _
Method: _
EX 2: Simplify.
(a)
( x 6)( x 8) (b) (4a+5
Volumes of Pyramids and Cones
The volume of a pyramid or cone is one-third that of a prism or cylinder with the same
base area and height. So.
V =1 Bh
3
(where B is the area of the base)
*THINK OF THE RICE!*
EX 1: Find the volume of the square
pyramid bel
Surface Areas of Pyramids & Cones Notes
For non-regular pyramids (with different faces), you have to find the area of each face to
find the lateral area. Add in the area of the base to find the surface area.
For regular pyramids and right cones, there is
Means and Midpoints Review
Suppose you want the average (mean) of two test grades. Add and divide by 2.
Same idea as finding the midpoint of two coordinates on the number line.
Number Line Midpoint Formula: The midpoint of the segment with endpoints a and
Equations for Circles
The equation for a circle with center (h, k) and radius r, is the set of points (x,y) where
( x h) 2 ( y k ) 2 r 2
Why does this work?
The radius is the distance from (h,k) to (x,y).
Use the distance formula to find a formula for the
Area of a Circle
Area of a circle: A r 2
EX 1: A rotating lawn sprinkler shoots water a distance of 10 meters. What is the area of
the region where it waters?
Probability of randomly hitting the bull's-eye of a target is
Area (bull's-eye)
-Area (whole tar
Prisms and Cylinders Review
polygon (boundary):
polygonal region: (includes interior)
surface (carton or box)
rectangular solid (brick)
A box has six faces. Opposite faces lie in parallel planes.
Face rectangular region that forms the surface of a box
cub
Polyhedrons & Nets Study Guide
polyhedron: Union of polygons with no holes. (The 3-D counterpart of polygons.)
Pyramids and prisms are polyhedra
Cylinders and cones are NOT polyhedra
Polyhedrons (or polyhedra) are classified by the number of sides (face
Areas of Right Triangles Notes
Area of a Right Triangle
=
1
bh
2
Below is a right triangle. Its area is half of a rectangle with sides b and h.
h
b
Area of non-right triangles
Altitude: perpendicular segment from a vertex to the line containing the opposi
Spheres and Sections Notes
sphere: the set of points in space at a certain distance (its radius) from a point (its center).
(The sphere is the 3-D counterpart of the circle.)
solid sphere - shade in - baseball
outline of a sphere - don't shade - bubble
A