Geometry/Chapter 9

PrismsEdit

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.

 

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

PyramidsEdit

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.

CylindersEdit

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

ConesEdit

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.

SpheresEdit

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

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Chapter 8 · Geometry · Chapter 10