unit 14 - volume (theory)
TRANSCRIPT
![Page 1: Unit 14 - Volume (Theory)](https://reader034.vdocument.in/reader034/viewer/2022042605/577cc9b51a28aba711a4647b/html5/thumbnails/1.jpg)
A. POLYHEDRA
A polyhedron is a 3D shape bounded by polygons. These polygons are called faces.
The edges of a polyhedron are the lines where the faces meet.
Its vertices are the corners where the faces meet.
A regular polyhedron must meet two criteria:
+ Its faces are identical regular polygons.
+ The same number of faces meet at each of the polyhedron´s vertices.
![Page 2: Unit 14 - Volume (Theory)](https://reader034.vdocument.in/reader034/viewer/2022042605/577cc9b51a28aba711a4647b/html5/thumbnails/2.jpg)
A prism is a polyhedron bounded by two identical polygons, called bases, and several rectangles, called lateral faces. The height of a
prism is the distance between the bases.
A regular prism is a prism whose bases are regular polygons.
A cuboid is a polyhedron with six faces that are perpendicular to one another. Its faces are rectangles or squares (then called cube).
![Page 3: Unit 14 - Volume (Theory)](https://reader034.vdocument.in/reader034/viewer/2022042605/577cc9b51a28aba711a4647b/html5/thumbnails/3.jpg)
A pyramid is a polyhedron with a polygonal base and triangular lateral sides which meet at a vertex called the apex.
A regular pyramid is a pyramid whose base is a regular polygon and whose lateral sides are isosceles or equilateral triangles.
![Page 4: Unit 14 - Volume (Theory)](https://reader034.vdocument.in/reader034/viewer/2022042605/577cc9b51a28aba711a4647b/html5/thumbnails/4.jpg)
B. NON-POLYHEDRA (SOLIDS OF REVOLUTION)LID
A non-polyhedron is a solid where any surface is not flat. For example:
Some of the most non-polyhedra are the solids of revolution. A solid of revolution is 3D shape obtained when a plane shape rotates around a
straight line. This line is called the axis of revolution.
Cylinders, cones and spheres are the most known solids of revolution.
![Page 5: Unit 14 - Volume (Theory)](https://reader034.vdocument.in/reader034/viewer/2022042605/577cc9b51a28aba711a4647b/html5/thumbnails/5.jpg)
A cylinder is the solid of revolution that is generated when a rectangle rotates around of its sides.
A cone is the solid of revolution that is generated when a right-angled triangle rotates around of its cathetii or legs.
A sphere is the solid of revolution that is generated when a circle rotates around one of its diameters.
![Page 6: Unit 14 - Volume (Theory)](https://reader034.vdocument.in/reader034/viewer/2022042605/577cc9b51a28aba711a4647b/html5/thumbnails/6.jpg)
A cylinder is a geometric shape bounded by two identical circles, called bases, and a curved lateral face. The height of a cylinder is the
distance between its bases.
The lateral face of a cylinder (without its bases) is a rectangle whose dimensions are the height of the cylinder and the length of the base
circumference.
![Page 7: Unit 14 - Volume (Theory)](https://reader034.vdocument.in/reader034/viewer/2022042605/577cc9b51a28aba711a4647b/html5/thumbnails/7.jpg)
A cone is a geometric shape bounded by a plane circular base and a curved lateral face that ends in an apex.
The curved lateral face of a cone is a circular sector wherein:
+ The radius is the cone generatrix.
+ The sector arc length is the perimeter of the cone´s base.
In cones there is a “special” link between the radius of the base, the height of the cone and its generatrix. Pythagoras is to blame.
![Page 8: Unit 14 - Volume (Theory)](https://reader034.vdocument.in/reader034/viewer/2022042605/577cc9b51a28aba711a4647b/html5/thumbnails/8.jpg)
![Page 9: Unit 14 - Volume (Theory)](https://reader034.vdocument.in/reader034/viewer/2022042605/577cc9b51a28aba711a4647b/html5/thumbnails/9.jpg)
C. VOLUME
![Page 10: Unit 14 - Volume (Theory)](https://reader034.vdocument.in/reader034/viewer/2022042605/577cc9b51a28aba711a4647b/html5/thumbnails/10.jpg)
![Page 11: Unit 14 - Volume (Theory)](https://reader034.vdocument.in/reader034/viewer/2022042605/577cc9b51a28aba711a4647b/html5/thumbnails/11.jpg)
VOLUME OF PRISMS AND PYRAMIDS
![Page 12: Unit 14 - Volume (Theory)](https://reader034.vdocument.in/reader034/viewer/2022042605/577cc9b51a28aba711a4647b/html5/thumbnails/12.jpg)
VOLUME OF SOLIDS OF REVOLUTION