Transcript CUBE: Net Drawing

Chapter 12 – Surface Area
and Volume of Solids
Section 12.1– Space Figures and
Nets
Section 12.1
Polyhedron – a 3-D figure whose
surfaces are polygons.
Face – individual polygon of the
polyhedron.
Edge – is a segment that is formed by
the intersection of two faces.
Vertex – is a point where three or more
edges intersect.
Section 12.1
Net – a 2-D pattern that you can fold to
form a 3-D figure.
Euler’s Formula – the number of faces
(F), vertices (V), and edges (E) of a
polyhedron are related by the
formula:
F+V=E+2
CUBE: Net Drawing
CUBE: 3-Dimensional
Faces
Edge
Vertex
CYLINDER: Net Drawing
CYLINDER: 3-Dimensional
Faces
Edge
TRIANGULAR PRISM: Net Drawing
TRIANGULAR PRISM:
3-Dimensional
Faces
Edge
Vertex
RECTANGULAR PRISM: Net
Drawing
RECTANGULAR PRISM:
3-Dimensional
Faces
Edge
Vertex
HEXAGONAL PRISM: Net Drawing
HEXAGONAL PRISM:
3-Dimensional
Faces
Edge
Vertex
TRIANGULAR PYRAMID: Net
Drawing
TRIANGULAR PYRAMID: 3Dimensional
Altitude
Slant Height
SQUARE PYRAMID: Net Drawing
Slant Height
SQUARE PYRAMID: 3Dimensional
Slant Height
HEXAGONAL PYRAMID: Net
Drawing
HEXAGONAL PYRAMID: 3Dimensional
Slant Height
Altitude
Chapter 12 – Surface Area
and Volume of Solids
Section 12.2 – Surface Areas of
Prisms and Cylinders
Section 12.2
Prism – is a polyhedron with exactly
two congruent, parallel faces.
Bases – two congruent, parallel faces
of a prism.
Lateral Faces – additional faces of a
prism.
Altitude – is a perpendicular segment
that joins the planes of the bases.
Section 12.2
Height – the length of the altitude.
Right Prism – the lateral faces are
rectangles and a lateral edge is the
altitude of the prism.
Oblique Prism – at least one lateral
face is not a rectangle.
Lateral Area – is the sum of the area of
the lateral faces.
CUBE: 3-Dimensional
BASE
LATERAL
FACE
RECTANGULAR PRISM:
3-Dimensional
BASE
LATERAL
FACE
TRIANGULAR PRISM:
3-Dimensional
LATERAL
FACE
BASE
HEXAGONAL PRISM:
3-Dimensional
BASE
LATERAL
FACE
OBLIQUE PRISM:
3-Dimensional
BASE
LATERAL
FACE
ALTITUDE
Section 12.2
Surface Area – the sum of the lateral area
and the two bases.
Theorem 10-1 – the lateral area of a right
prism is the product of the perimeter of
the base and the height.
L.A. = ph
The surface area of a right prism is the
sum of the lateral area and the area of the
2 bases.
S.A. = L.A. + 2B
Section 12.2
Cylinder – is a three-dimensional
figure with exactly two congruent,
parallel faces.
Bases – two congruent, parallel faces
of a cylinder are circles.
Altitude – is a perpendicular segment
that joins the planes of the bases.
CYLINDER: 3-Dimensional
BASE
OBLIQUE CYLINDER: 3Dimensional
BASE
ALTITUDE
Section 12.2
Surface Area – the sum of the lateral area
and the two circular bases.
Theorem – the lateral area of a right prism is
the product of the circumference of the
base and the height of the cylinder.
L.A. = 2πrh or L.A. = πdh
The surface area of a right prism is the
sum of the lateral area and the area of the
2 bases.
S.A. = L.A. + 2B or S.A. = 2πrh + 2πr2
Chapter 12 – Surface Area
and Volume of Solids
Section 12.3 – Surface Areas and
Pyramids and Cones
Moving from Prisms/Cylinders
to Pyramids/Cones
Section 12.3
Pyramid – is a polyhedron in which one
face can be any polygon and the other
faces are triangles that meet at a common
vertex.
Bases – the only face of a pyramid that is
not a triangle.
Lateral Faces – triangles of pyramid.
Vertex of a pyramid – the point where all
lateral faces of a pyramid meet.
Section 12.3
Altitude – is a perpendicular segment from
the vertex to the plane of the base.
Height – the length of the altitude (h).
Regular Pyramid – a pyramid whose base is
a regular polygon and whose lateral faces
are congruent isosceles triangles.
Slant Height – is the length of the altitude of
a lateral face of a pyramid.
Lateral Area – is the sum of the area of the
congruent lateral faces.
TRIANGULAR PYRAMID: 3Dimensional
Altitude
Slant Height
SQUARE PYRAMID: 3Dimensional
Slant Height
HEXAGONAL PYRAMID: 3Dimensional
Slant Height
Altitude
Section 12.3
Surface Area – the sum of the lateral area
and the area of the base.
Theorem – the lateral area of a regular
pyramid is the half the product of the
perimeter of the base and the slant height.
L.A. = ½ pl
The surface area of a regular pyramid is
the sum of the lateral area and the area of
the base.
S.A. = L.A. + B
Section 12.3
Cone – is a “pointed” like a pyramid, but its
base is a circle.
Right Cone – the altitude is a perpendicular
segment from the vertex to the center of
the base.
Bases – the only circle on a cone.
Vertex of a cone – the only distinctive point
on the object.
Section 12.3
Altitude – is a perpendicular segment from
the vertex to the plane of the base.
Height – the length of the altitude (h).
Slant Height – is the distance from the
vertex to a point on the edge of the base.
Lateral Area – is ½ the perimeter
(circumference) of the base times the slant
height.
CONE: Net Drawing
CONE: 3-Dimensional
Section 12.3
Surface Area – the sum of the lateral area
and the area of the base.
Theorem – the lateral area of a right cone is
the half the product of the circumference
of the base and the slant height.
L.A. = ½ 2rl or rl
The surface area of a right cone is the sum
of the lateral area and the area of the base.
S.A. = L.A. + B
Chapter 12 – Surface Area
and Volume
Section 12.6 – Surface Area and
Volumes of Spheres
Section 12.6
Sphere
Set of all points equidistant from a given
point.
C
Section 12.6
Surface Area of a Sphere
S = 4πr 2
C