Volume

1
Volume

• A polyhedron is a solid with polygonal faces
• As for polygons, the specific names are based on
  the number of faces
• For example, an heptahedron has 7 faces
• Some special cases
• A polyhedron with 4 faces is called a tetrahedron
• A hexahedron with congruent square faces is a
  cube
• A sphere is the set of all points in space
  equidistant from a center point
• A hemisphere is a sphere cut in half by a plane
  passing through its center

2
Volume

• The volume of a solid is the measure of the
  amount of space contained in the solid
• A volume of one cubic unit is the space enclosed
  by a cube with each edge one unit in length
• You could find the volume of a solid by counting
  the number of unit cubes that fit inside it
• Calculating volume usually requires three factors
• In cylinders, cones, or spheres, the radius
  appears as a factor multiple times
• A prism or pyramid may be slanted, or oblique
• Its volume is the same as a right prism or
  pyramid with the same base and height

Length 1 unit
Area 1 square unit
Volume 1 cubic unit
3
Volume

• The volume of a prism is the area of the base
  times the height of the prism
• The volume of a rectangular prism is given by the
  formula V lwh, where l is length, w is width,
  and h is height of the prism
• For a polygonal prism, the volume is given by the
  formula V BH, where B is the area of the base
  and H is height of the prism
• For a cylinder, the volume is given by the
  formula V pr2h,
• where r is the radius of the base and h is the
  height of the cylinder
• The volume of a pyramid is 1/3 of the volume of a
  prism with a congruent base and the same height
• For a polygonal pyramid, the volume is given by
  the formula V 1/3BH, where B is the area of the
  base and H is height of the pyramid
• For a cone, the volume is is given by the formula
  V 1/3pr2h
• The volume of a sphere is is given by the formula
  V 4/3pr3
• The surface area of a sphere is is given by the
  formula SA 4pr2