Section 12.1 Three Dimensional Figures
Polyhedron: a solid bounded by polygons called faces. (plural is polyhedra or polyhedrons)
Edge: a segment formed by the intersection of two faces.
Vertex: a point where three of more edges meet. (plural is vertices)
Regular Polyhedron: all faces are regular polygons.
Types of Geometric Solids:
Prism (a polyhedron): has 2 parallel congruent faces called bases. All other faces are quadrilaterals. Prisms are named by their bases. (for example triangular prism, rectangular prism, hexagonal prism)
Pyramid (a polyhedron): has one base. All other faces are triangles that intersect at one vertex. Pyramids are named by their bases. (for example triangular pyramid, square pyramid, pentagonal pyramid)
Cylinder: has 2 parallel congruent circular faces called bases. The lateral surface is a rolled up rectangle
Cone: has 1 circular face called a base. The lateral surface is a rolled up sector.
Sphere: essentially a ball.
Platonic Solids
Tetrahedron


Cube


Octahedron


Dodecahedron


Icosahedron

Faces + Vertices = Edges + 2
OR
F + V = E + 2
F = E + 2 – V
V = E + 2 – F
E = F + V – 2
Section 12.2 Nets and Surface Area
Section 12.3 Surface Area of Prisms
Prism: a polyhedron with two congruent faces (called bases) lying in parallel planes.
the other faces (called lateral faces) are parallelograms connecting the vertices of the bases. The parallel segments connecting these vertices are called lateral edges.
Right Prism: contains lateral edges that are perpendicular to the bases.
Oblique Prism: contains lateral edges that are not perpendicular to the bases.
Surface Area of a Polyhedron: is the sum of the areas of all the faces.
Lateral Area of a Polyhedron: is the sum of the areas of all the lateral faces.
Surface Area (S) = 2 * Base Area (B) + Perimeter of the base (P) * Height of the prism (h)
OR: S = 2B + Ph
Lateral Area of a Right Prism
Lateral Area (L) = Perimeter of the base (P) * Hieght of the Prism (h)
Or: L = Ph
The 5 steps to calculate Surface Area of Prisms
2. Record the height of the prism. (h=___)
3. Calculate the area of the base. (B=___)
4. Calculate the perimeter of the base. (P=___)
5. Plug and calculate the Surface area using S = 2*B + P*h
Triangular Prism
Section 12.4 Surface Area of Cylinders
Surface Area (S) = 2*Base Area (B) + Circumference (C) * Height (h)
OR: S = 2B + Ch
OR: S =
2*Π*r^2 + 2*
The 5 steps to calculate Surface Area of Cylinders
2. Record the height of the cylinder. (h=___)
3. Calculate the area of the base. (B=___)
4. Calculate the circumference of the base. (C=___)
5. Plug and calculate the Surface area using S = 2*B +
C*h
Surface Area (S) = Base Area (B) + ˝ * Perimeter (P) * Slant Height (l)
OR: S = B + ˝ Pl
The 5 steps to calculate Surface Area of Pyramids
1. Draw and label the base. (All Bases
are Regular)
2. Calculate (or record) the slant height of the pyramid. (l=___)
3. Calculate the area of the base. (B=___)
4. Calculate the perimeter of the base. (P=___)
5. Plug and calculate the Surface area using S = B + 1/2*P*l
Square Based Pyramid
Pentagonal Based Pyramid
Section 12.6 Surface Area of Cones
Surface Area (S) = Base Area (B) + 1/2 * Circumference (C) * Slant Height (l)
OR: S = B + 1/2 Cl
The 5 steps to calculate Surface Area of Cones
1. Draw and label the base.
2. Calculate the slant height of the cone. (l=___)
3. Calculate the area of the base. (B=___)
4. Calculate the circumference of the base. (C=___)
5. Plug and calculate the Surface area using S =B +
1/2*C*l
Sphere with a Circumference = 60
Hemisphere with a radius = 12
Hemisphere with a great circle area = 800
Chapter 13 notes Volume
Section 13.1 Volume of Prisms and Cylinders
Volume of a Prism (V) = Base Area (B) * Height (h)
The 4 steps to calculate Volume of Prisms and Cylinders
1. Draw and label the base.
2. Record the height of the prism or cylinder. (h=___)
3. Calculate the area of the base. (B=___)
4. Plug and calculate the Volume using V = B * h
Section
13.2 Volume of Pyramids and Cones
Volume of a Pyramid (V) =1/3 * Base Area (B) * Height (h)
The 4 steps to calculate Volume of Pyramids and Cones
1. Draw and label the base.
2. Calculate the height of the pyramid or cone. (h=___)
3. Calculate the area of the base. (B=___)
4. Plug and calculate the Volume using V = 1/3 * B * h
Section 13.4 Congruent and Similar Solids
Solids are similar if and only if their corresponding measurements are all in the same ratio.
Solids are congruent if and only if their corresponding measurements are all equal.
Theorem 13.1: If two solids are similar with a scale factor of a : b, then the surface areas have a ratio of a^2 : b^2 and the volumes have a ratio of a^3 : b^3
Example
If the side ratio/scale factor is 3/4,
then the surface area ratio is 9/16 (square the side ratio)
and the volume ratio is 27/64 (cube the side ratio)