Solid Figures

1
Solid Figures
2
12.1
Polyhedrons
A solid bound by polygons that enclose a single
region of space.
A polyhedron CANNOT have any curved sides.
3
Determine which of the following is a polyhedra.
4
Faces
6 Faces
How many polygons make up the polyhedron
5
Edges
12 Edges
A line segment formed by the intersection of two
faces
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Vertex
8 Vertex
A point where three or more edges meet
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Euler's Theorem
F V E 2
Faces (F) Vertices (V) Edges (E) 2
8
Use Eulers formula to solve for the following

• F 20
• V 8
• E

F V E 2
20 8 E 2
28 E 2
26 E
9
Count the number of faces, vertices, and edges.
4
4
6
10
Regular Tetrahedron
(the net)
Four Regular Triangles
11
Cube
(the net)
Four Regular Quadrilaterals
12
Regular octahedron
(the net)
Eight Regular Triangles
13
Regular dodecahedron
(the net)
Twelve Regular Pentagons
14
Regular icosahedron
(the net)
Twenty Regular Triangles
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Prisms
Pyramids

• Have 2 bases
• Named by the shape of the bases

• Have 1 base
• Lateral faces meet at one point
• Named by the shape of the base

Pentagonal Prism
Hexagonal Pyramid
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12.6 Surface Area and Volume of Spheres
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Radius of a Sphere
r
18
If you cut a sphere right down the middle you
would create two congruent halves called
HEMISPHERES.
You can think of the globe. The equator cuts the
earth into the northern and southern hemisphere.
19
Look at the cross section formed when you cut a
sphere in half.
What shape is it?
A circle!!! This is called the GREAT CIRCLE of
the sphere.
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Formulas for a Sphere
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The circumference of a great circle of a sphere
is 25 inches. Find the surface area of the
sphere. (Round to the nearest tenths.)
25 in
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Surface Area of a Sphere (round to the nearest
hundredths)
8 in
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Surface Area of a Sphere (round to the nearest
hundredths)
10 cm
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Volume of a Sphere (round to the nearest
hundredths)
2 cm
25
Volume of a Sphere
10 cm
26
pg. 723 6-18, 54, 55 pg. 762 10-17, 20-26