Geometry/Chapter 9
Prisms[edit  edit source]
An nsided prism is a polyhedron made of an nsided polygonal base, a translated copy, and n faces joining corresponding sides. Thus these joining faces are parallelograms. All crosssections parallel to the base faces are the same. A prism is a subclass of the prismatoids.
The volume of a prism is the product of the area of the base and the distance between the two base faces, or height. In the case of a nonright prism, the height is the perpendicular distance.
In the following formula, V=volume, A=base area, and h=height.
The surface area of a prism is the sum of the base area and its face, and the sum of each side area, which for a rectangular prism is equal to:

 where l = length of the base, w = width of the base, h = height
Pyramids[edit  edit source]
The volume of a Pyramid can be found by the following formula:
 A = area of base, h = height from base to apex
The surface area of a Pyramid can be found by the following formula:
 = Surface area, = Area of the Base, = Perimeter of the base, = slant height.
Cylinders[edit  edit source]
The volume of a Cylinder can be found by the following formula:
 r = radius of circular face, h = distance between faces
The surface area of a Cylinder including the top and base faces can be found by the following formula:
 is the radius of the circular base, and is the height
Cones[edit  edit source]
The volume of a Cone can be found by the following formula:
 r = radius of circle at base, h = distance from base to tip
The surface area of a Cone including its base can be found by the following formula:
 is the radius of the circular base, and is the height.
Spheres[edit  edit source]
The volume of a Sphere can be found by the following formula:
 r = radius of sphere
The surface area of a Sphere can be found by the following formula:
 r = radius of the sphere
 Geometry Main Page
 Motivation
 Introduction
 Geometry/Chapter 1  HS Definitions and Reasoning (Introduction)
 Geometry/Chapter 1/Lesson 1 Introduction
 Geometry/Chapter 1/Lesson 2 Reasoning
 Geometry/Chapter 1/Lesson 3 Undefined Terms
 Geometry/Chapter 1/Lesson 4 Axioms/Postulates
 Geometry/Chapter 1/Lesson 5 Theorems
 Geometry/Chapter 1/Vocabulary Vocabulary
 Geometry/Chapter 2 Proofs
 Geometry/Chapter 3 Logical Arguments
 Geometry/Chapter 4 Congruence and Similarity
 Geometry/Chapter 5 Triangle: Congruence and Similiarity
 Geometry/Chapter 6 Triangle: Inequality Theorem
 Geometry/Chapter 7 Parallel Lines, Quadrilaterals, and Circles
 Geometry/Chapter 8 Perimeters, Areas, Volumes
 Geometry/Chapter 9 Prisms, Pyramids, Spheres
 Geometry/Chapter 10 Polygons
 Geometry/Chapter 11
 Geometry/Chapter 12 Angles: Interior and Exterior
 Geometry/Chapter 13 Angles: Complementary, Supplementary, Vertical
 Geometry/Chapter 14 Pythagorean Theorem: Proof
 Geometry/Chapter 15 Pythagorean Theorem: Distance and Triangles
 Geometry/Chapter 16 Constructions
 Geometry/Chapter 17 Coordinate Geometry
 Geometry/Chapter 18 Trigonometry
 Geometry/Chapter 19 Trigonometry: Solving Triangles
 Geometry/Chapter 20 Special Right Triangles
 Geometry/Chapter 21 Chords, Secants, Tangents, Inscribed Angles, Circumscribed Angles
 Geometry/Chapter 22 Rigid Motion
 Geometry/Appendix A Formulae
 Geometry/Appendix B Answers to problems
 Appendix C. Geometry/Postulates & Definitions
 Appendix D. Geometry/The SMSG Postulates for Euclidean Geometry