Solid Mensuration

Description:

    Concept of lines and planes; Cavalieri's and Volume theorems; formulas for areas of plane figures, volumes for solids; volumes and surfaces areas for spheres, pyramids, and cones; zone, sector, and segment of a sphere; theorems of Pappus.

Overview:

    Solid Geometry (also known as Solid Mensuration) is the study of various solids. It is the study of the measure of volume, area, height, length, and many more. This subject is used extensively in the practice of engineering. The knowledge of this subject is a necessity for engineers in any project construction. Understanding objects in three-dimensional space help engineers create models and scenarios and solve problems mathematically before ever actually using or building any resources.

    Mensuration is the mathematical name for calculating the areas, volumes, length of sides, and other geometric parts of standard geometric shapes such as circles, spheres, polygons, prisms, cylinders, cones, etc., through the use of mathematical equations or formulas. Included here are the most frequently used and important mensuration formulas for the common geometric figures, both plane and solid.

Read More:
(1) Solid Geometry - Math is Fun

(2) Chapter 2: Mensuration of Plane and Solid Figures

(3) 11.5: Lines and Planes in Space - Mathematics LibreTexts
(4) Introduction to Conic Sections | Boundless Algebra

(5) Solid geometry vocabulary (article) | Khan Academy

Watch:
(1) Points, Lines, Planes, Segments, & Rays - Collinear vs Coplanar Points - Geometry

     by The Organic Chemistry Tutor [14:25] | YouTube

(2) Area of a Rectangle, Triangle, Circle & Sector, Trapezoid, Square, Parallelogram, Rhombus, Geometry

     by The Organic Chemistry Tutor [20:34] | YouTube

(3) Introduction to Solids || Plane & Solid Mensuration Explained in Filipino

      by Mathuklasan with Sir Ram [11:47] | YouTube

(4) Volume and Surface Area of a Sphere Formula, Examples, Word Problems, Geometry

      by The Organic Chemistry Tutor [11:08] | YouTube

(5) Volume of a Cone and Pyramid - How to Find (Formula)

      by Mario's Math Tutoring [2:59] | YouTube

Topics:

1. Plane Figures
        a. Mensuration of Plane Figures

2. Lines and Planes in Space
        a. Typical Proofs of Solid Geometry
        b. Angles

3. Solids for which V = Bh
        a. Solid Sections
        b. Cubes
        c. Rectangular Parallelopiped
        d. Cavalieri's Theorem
        e. Volume Theorem
        f. Prism
        g. Cylindrical Surface
        h. Cylinder (Circular and Right Circular)

4. Solids for which V = 1/3 Bh
        a. Pyramids
        b. Similar Figures
        c. Cones
        d. Frustum of Regular Pyramid
        e. Frustum of Right Circular Cone

5. Sphere
        a. Surface Area and Volume
        b. Zone
        c. Segment
        d. Sector

6. Theorems of Pappus

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