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Solids Notes
Important Terms
Term
Prism
Right Prism
Foot of the Height
Lateral/Cylindrical Surface
Lateral/Conical Surface
Apex
Definition
A three-dimensional shape
A three-dimensional shape that has 90°
vertical angles
The bottom side of a shape
The sides of a prism that you can wrap
your hand around
The vertical edges of a prism
The corner of a prism
How tall is the shape
When you unfold a prism into a flat
shape
The sum of the areas of all the lateral
sides of a prism
The sum of the areas of all the sides of a
prism (bases and lateral sides)
The length of the lateral edge of a
pyramid
The center of the base of a pyramid
The curved side of a cylinder
The curved side of a cone
The point at the top of a pyramid/cone
Important Symbols used in Formulas
Symbol
Al
At
Ab
Pb
h
a
r
d
Meaning
Lateral Area
Total Area
Base Area
Perimeter of the base
Height of the prism
Slant Height
Radius
Diameter
Base
Lateral Faces
Lateral Edge
Vertex
Height
Net
Lateral Area
Total Area
Slant Height
Important Formulas
Name
Lateral Area of a
Right Prism
Total Area of a
Right Prism
Lateral Area of a
Pyramid
Total Area of a
Pyramid
Lateral Area of a
Cylinder
Main Formula
Reworked #1
Reworked #2
or
Total Area of a
Cylinder
or
Lateral Area of
Circular Cone
Total Area of a
Circular Cone
or
Surface Area of a
Sphere
Important Properties about Prisms
Right Prisms
 Opposite sides of a prism are parallel
 The lateral sides are perpendicular to the bases
 Opposite sides and edges are congruent
Right Regular Pyramids
 The base of a pyramid can be different regular polygons
 The lateral faces are isosceles triangles (two sides of the triangle are equal)
 A pyramid is right and regular when the foot of the height is at the center of
the base. Or in other words, when the apex is directly over the center of the
base.
 The slant height is the height of one of the triangles that make up the lateral
faces. A slant height goes from the apex to the midpoint of one the sides of
the base.
Right Circular Cylinders
 The radii of the top and bottom are equal
 The radius of the base is also the radius of the cylinder
 The net of a cylinder unfolds into two circles and a rectangle
Right Circular Cones
 Cones only have circles(disc) as a base
 The radius of the base is the radius of the cone
 The height of the cone is from the center of the base to the apex of the cone
 Any line joining the edge of the circle to the apex is a slant height
Spheres
 The radius of a sphere extends from center of the sphere to any point on the
sphere
 A diameter of a sphere is a line that connects any two point on a sphere so
long as it passes through the center of the sphere (O).
 To find the surface area of a hemisphere, divide by two and add the area of
the disc.
Strategies for Answering Questions
Find the Net of a Prism
 When finding the net of a prism, imagine cutting a box open so that it would
lay flat on the ground
 Then look for the different smaller shapes that make up the bigger prism
(E.g. squares, rectangles, triangles)
 Find the area of each smaller shape
 Then add all the smaller shapes together to find the total area
Decomposable Solids
 The point of decomposable solid questions is to add or subtract the areas of
different solids together.
 The best strategy is break down the shape into smaller parts and make an
equation.
 Ex: A right prism + regular pyramid = Total area
 It very important to remember that the only the outside parts of the shape
count towards the total area.
 If you can’t touch it, it is not part of the total area.
 All prisms can be divided into smaller sections so consider that when
working with the formulas.