Geometry/Chapter 9

Prisms An n-sided prism is a polyhedron made of an n-sided polygonal base, a translated copy, and n faces joining corresponding sides. Thus these joining faces are parallelograms. All cross-sections parallel to the base faces are the same. A prism is a subclass of the prismatoids. The volume of a prism is the product of the area of the base and the distance between the two base faces, or height. In the case of a non-right prism, the height is the perpendicular distance. Image:Square Prism Labeled.png In the following formula, V=volume, A=base area, and h=height. The surface area of a prism is the sum of the base area and its face, and the sum of each side area, which for a rectangular prism is equal to: where l = length of the base, w = width of the base, h = height Pyramids The volume of a Pyramid can be found by the following formula: A = area of base, h = height from base to apex The surface area of a Pyramid can be found by the following formula: = Surface area, = Area of the Base, = Perimeter of the base, = slant height. Cylinders The volume of a Cylinder can be found by the following formula: r = radius of circular face, h = distance between faces The surface area of a Cylinder including the top and base faces can be found by the following formula: is the radius of the circular base, and is the height Cones The volume of a Cone can be found by the following formula: r = radius of circle at base, h = distance from base to tip The surface area of a Cone including its base can be found by the following formula: is the radius of the circular base, and is the height. Spheres The volume of a Sphere can be found by the following formula: r = radius of sphere The surface area of a Sphere can be found by the following formula: r = radius of the sphere Chapter 8 Chapter 10 Geometry (book)