Transcript Applied Geometry
Geometry
Lesson 1 – 7 Three-Dimensional Figures Objective: Identify and name three-dimensional figures.
Find surface area and volume.
Polyhedrons
Polyhedrons A solid with all flat surfaces that enclose a single region of space.
Face – each flat surface Edges – the line segment where the faces intersect Vertex – the point where 3 or more edges intersect
Types of Solids: Prism
A polyhedron with 2 parallel and congruent faces called
bases
Bases are connect by parallelogram faces This is one example of a prism Named using the bases: Pentagonal Prism
Naming Prisms
Triangular Prism Rectangular Prism
Types of Solids: Pyramid
A polyhedron that has a polygonal base and three or more triangular faces that meet at a common point.
One example: Rectangular Pyramid
Naming Pyramids
Triangular Pyramid Rectangular Pyramid Pentagonal Pyramid
Types of Solids: Cylinder
Not a polyhedron A solid with congruent parallel circular bases connected by a curved surface.
Types of Solids: Cone
Not a polyhedron A solid with a circular base connected by a curved surface to a single vertex.
Types of Solids: Sphere
Not a polyhedron A set of points in space that are the same distance from a given point. A sphere has no faces, edges, or vertices.
Determine whether the solid is a polyhedron, if yes, name the bases, faces, edges, and vertices.
Yes a polyhedron Bases: MNOP & RSTQ *Use the ‘top’ and ‘bottom’ on Rectangular prisms for the bases.
Faces: MNOP, RSTQ, Remember to include the bases MRQP, RSNM, STON, PQTO Edges:
MN RS ST NO QT PO MP RQ RM SN TO QP
Vertices: R, M, S, N, T, O, Q, P
Determine whether the solid is a polyhedron, if yes, name the bases, faces, edges, and vertices.
Not a polyhedron
Determine whether the solid is a polyhedron, if yes, name the bases, faces, edges, and vertices.
Bases: GHI & JKL Faces: GHKJ, HKLI, & GJLI Vertices: G,H,K,J,L,I
Regular Polyhedron
A polyhedron with all faces regular polygons and all edges congruent.
Can you think of a regular polygon?
Regular Polyhedrons: Platonic Solids
Regular Polyhedrons: Platonic Solids
Area & Volume
Lateral Area – area of the lateral faces (faces that are not bases) Surface Area (Total Area) – is the area of the whole figure Lateral area + area of bases Volume – the measure of the amount of space enclosed by a solid figure.
Hands-on Activity
Using the geometric solids set Find formulas for the following for all solids Lateral Area Surface Area (Total Area) Volume
Find Surface area and Volume
Square Pyramid Surface area (Total Area): write formula first 1
T
P
B
2 Find P and B first P = 4(6) = 24 B = 6*6 = 36
T
1 2 = 96 cm 2 Plug into formula 36 Continued…
Continued
…
Volume
V
1 3
Bh
Remember B = 36
V
1 3
= 48 cm
3
Find Surface area & Volume
T
2 2
rh
2
r
2 2
2 216 288
cm
2 72 904 .
8
cm
2 Need to have both!
V
6
r
2 2
h
648 2035 .
8
cm
3 Need to have both!
T
Find Surface Area & Volume
Ph
2
B
P = 2(5.2) + 2(10) = 30.4
B = (5.2)(10) = 52 T = (30.4)(6) + 2(52) = 286.4 cm 2 V = Bh = (52)(6) = 312 cm 3
Find the Surface Area & Volume
T
255
r
r
2 225
2 480
1508 .
0
in in
2 2 1507.96 rounded up to 1508.0
V
1 1 3 3 600
r in
2 3
h
1885 .
0
in
3 1884.95 rounded up
The diameter of the pool Mr. Sato purchased is 8 feet. The height of the pool is 20 inches. Find each measure to the nearest tenth.
Surface Area of pool *Be careful dealing with feet and inches!
T
2
rh
2
r
2 We don’t need 2 bases since the pool Does not have a top 2 2 13 1 3 1 3 16 2 20 inches is 1 2/3 feet 29 1 3
sq in
92 .
2
sq in
Volume of water needed to fill the pool to a depth of 16 inches.
Be careful with feet and inches!
V
r
2
h V
2 1 1 3 21 1 3
cubic
67 .
0
cubic ft ft
16 inches is 1 1/3 feet