SMCHS
Geometry B
Chapter 12 Notes
Prism: solid with two polygonal bases.
Bases: the foundation of a solid. It takes the form of a polygon or a circle.
Altitude: the height of a solid. This is a different measurement from the height of the base.
Lateral faces: the side of a solid which connects a base to a point or another base
Lateral edges: the line that joins to lateral faces
Oblique prism: a prism in which the bases do not lie directly on top of each other (slanted)
Right prism: a prism with 90 degree angles between the base and the lateral faces
Lateral area: the area of the lateral faces
Total area: the surface area of a solid.
Pyramid: solid with a single base. All lateral faces meet at a single point above the base
Vertex: the point where all the lateral faces meet in a pyramid
Regular pyramids: a pyramid with a regular polygon as a base
Slant height: the length from a base edge to the vertex of a pyramid or cone
Cylinder: a solid with two circular bases
Right cylinder: a solid with two circular bases which form 90 degree angles with lateral face
Radius: the distance from the center of a circle to the edge of a circle
Cone: a pyramid with a circular base instead of a polygon
Theorem 12-1:
The lateral area of a right prism equals the perimeter of the base times the height of the prism.
Theorem 12-2:
The volume of a right prism equals the area of a base times the height of the prism.
Theorem 12-3:
The lateral area of a regular pyramid equals half the perimeter of the base times the slant height.
Theorem 12-4:
The volume of a pyramid equals one third the area of a base times the height of the pyramid.
Theorem 12-5:
The lateral area of a cylinder equals the circumference of a base times the height of the cylinder.
Theorem 12-6:
The volume of a cylinder equals the area of a base times the height of the cylinder.
Theorem 12-7:
The lateral area of a cone equals half the circumference of the base times the slant height.
Theorem 12-8:
The volume of a cone equals one third the area of the base times the height of the cone.
Theorem 12-9:
The area (surface area) of a sphere equals times the square of the radius.
Theorem 12-10:
The volume of a sphere equals times the cube of the radius.
Theorem 12-11:
If the scale factor of two similar solids is a:b, then:
(1)The ratio of corresponding perimeters is.
(2)The ratio of the base areas, of the lateral areas, and of the total areas is.
(3)The ratio of the volumes is.