1. Chapter 9
Geometry
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Chapter 9: Geometry
9.1 Points, Lines, Planes, and Angles 9.2 Curves, Polygons, and Circles 9.3 Perimeter, Area, and Circumference 9.4 The Geometry of Triangles: Congruence, Similarity, and the Pythagorean Theorem 9.5 Space Figures, Volume, and Surface Area 9.6 Transformational Geometry 9.7 Non-Euclidean Geometry, Topology, and Networks 9.8 Chaos and Fractal Geometry
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3. Section 9-5 Chapter 1 Space Figures, Volume, and Surface Area
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4. Space Figures, Volume, and Surface Area
Volume and Surface Area of Space Figures
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Space Figures
Space figures take three dimensions of space to represent the figure.
One important group of space figures is a group called polyhedra. The faces of these figures are made only of polygons.
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6. Regular Polyhedra (Platonic Solids)
Name
Description
Tetrahedron
4 equilateral triangles
Hexahedron
6 squares (cube)
Octahedron
Groups of 4 regular triangles
Dodecahedron
Groups of 3 regular pentagons
Icosahedron
Groups of 5 regular triangles
See pictures on the next slide.
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Space Figures
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Space Figures
The next slide shows space includes two other polyhedra: pyramids and prisms. Pyramids are made of triangular sides and a polygonal base. Prisms have two faces in parallel planes; these faces are congruent polygons.
The next slide also shows a torus which is a doughnut-shaped solid and figures made up in part of circles including right circular cones and right circular cylinders.
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Space Figures
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10. Volume and Surface Area
Volume is a measure of capacity of a space figure. Volume is measured in cubic units.
Surface Area is the total area that would be covered if the space figure were “peeled” and the peel laid flat. Surface area is measured in square units.
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11. Volume of Surface Area of a Box
The volume V and surface area S of a box with length l, width w, and height h is given by the formulas h w l
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12. Example: Volume of Surface Area of a Box
Find the volume and surface area of the box below.
3 in.
2 in.
7 in.
Solution
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13. Volume of Surface Area of a Cube
The volume V and surface area S of a cube with edge of length s is given by the formulas s s s
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14. Example: Volume of Surface Area of a Cube
Find the volume and surface area of the cube below.
Solution
5 ft.
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15. Volume of Surface Area of a Right Circular Cylinder
The volume V and surface area S of a right circular cylinder with base radius r and height h is given by the formulas h r
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16. Example: Volume of Surface Area of a Right Circular Cylinder
Find the volume and surface area of the cylinder below.
10 m
Solution
2 m
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17. Volume of Surface Area of a Sphere
The volume V and surface area S of a sphere radius r is given by the formulas r
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18. Example: Volume of Surface Area of a Sphere
Find the volume and surface area of the sphere below.
9 in.
Solution
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19. Volume of Surface Area of a Right Circular Cone
The volume V and surface area S of a right circular cone with base radius r and height h is given by the formulas h r
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20. Example: Volume of Surface Area of a Right Circular Cone
Find the volume and surface area of the cone below.
4 m
3 m
Solution
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Volume of a Pyramid
The volume V of a pyramid with height h and base of area B is given by the formulas h
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22. Example: Volume of a Pyramid
Find the volume and surface area of the pyramid (rectangular base) below.
7 cm
Solution
3 cm
6 cm
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