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Surface Area and Volume

Proofs/Supplementary Lessons

Volume of a Sphere  Tutorial Name Tutorial Description Surface Area of a Frustum Derivation of the formula for the surface area of a frustum. Surface Area of a Sphere Derivation of the formula for the surface area of a sphere using frustums. Volume of a Sphere Derivation of the formula for volume of a sphere using volumes of pyramids.

Tutorials

 Tutorial Name Tutorial Description Surface Area and Volume (Part-1) Descriptoin of polyhedra including pyramids, prisms, cylinders and cones, classifying polyhedra, cross sections, introduction to conic sections, introduction to solids of revolution. Surface Area and Volume (Part-2) Lateral and surface area of prisms.  Net of a prism and an introcuction to oblique prisms. Surface Area and Volume (Part-3) Lateral and surface area of cylinders.  Net of a cylinder.  Lateral and surface of composit solids including cylinders.  Effects of changing dimensions on surface area. Surface Area and Volume (Part-4) Lateral and surface area of pyramids.  Computing lateral and surface area of regular pyramids. Surface Area and Volume (Part-5) Lateral and surface area of rectangular pyramids.  Lateral and surface area of cones.  Introduction to oblique cones. Surface Area and Volume (Part-6) Examples of computing lateral and surface area of cones.  Lateral and surface area of composit solids including cones.  Introduction to volume of three dimensional solids.  Derivation of the formula for volume of a pyramid. Cavalierie's Principle. Surface Area and Volume (Part-7) Examples of computing volumes of prisms, cylinders (both right and oblique), pyramids, and cones. Surface Area and Volume (Part-8) Examples of computing volumes of composite solids.  Effects on volume by changing dimensions. Surface Area and Volume (Part-9) Surface area volume of spheres.  Example of finding surface and volume of a sphere and a composite solid including spheres. Surface Area and Volume (Part-10) Comparison of Euclidian and non-Euclidian geometries.  Introduction of spherical geometry.  Length of a spherical arc.  Area of a spherical triangle. Chapter 12 Review (1-8) Worked out solutions to problems 1-8 Chapter 12 Review (9-13) Worked out solutions to problems 9-13 Chapter 12 Review (14-17) Worked out solutions to problems 14-17 Chapter 12 Review (18-24) Worked out solutions to problems 18-24 Chapter 12 Review (25-29) Worked out solutions to problems 25-29 Chapter 12 Review (30-32) Worked out solutions to problems 30-32