9.5 Space Figures, Volume, and Surface Area Part 1: Volume

Space Figures Space figures are three dimensional solids. The faces are the flat sides which meet at edges. The “corners” are called vertices. Solids whose faces are polygons are called polyhedra. – The faces of a regular polyhedra are all one kind of regular polygon.

Regular Polyhedra (a.k.a. Platonic Solids) A tetrahedron is composed of four equilateral triangles. A cube (or hexaherdon) is composed of six squares. An octahedron is formed by eight equilateral triangles. A dodecahedron is formed by twelve regular pentagons. An icosahedron is made up of twenty equilateral triangles.

Volume While area is a measure of surface covered by a plane figure, volume is a measure of capacity of a space figure. – In other words, how much “stuff” fits INSIDE the figure. Volume is measured in cubic units (m 3, ft 3, etc.)

Volume of a Box (IB: Cuboid) If a box has length ℓ, width w, and height h., then the volume V is given by V = ℓwh.  Find the volume of the box shown.

Volume of a Right Circular Cylinder If a right circular cylinder has height h and radius of its base equal to r, then the volume V is given by V = πr 2 h.  A right circular cylinder has a height of 18 in. and radius of 6 in. Find the volume.

Volume of a Sphere If a sphere has a radius r, then the volume V is given by V = 4 / 3 πr 3.  Find the volume of a sphere having a 3 meter radius.

Volume of a Right Circular Cone If a right circular cone has height h and radius of its circular base is r, then the volume V is given by V = 1 / 3 πr 2 h.  Find the volume of a cylinder with a base radius of 46 m and a height of 220 m.

Volume of a Pyramid If B represents the area of the base of a pyramid and h represents the height, then the volume V is given by V = 1 / 3 Bh.  Find the volume of the pyramid. The base is a rectangle.