Geometry/Chapter 9

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[edit] 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.

V = Ah

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:

  • SA = 2lw + 2lh + 2wh
    • where l = length of the base, w = width of the base, h = height

[edit] Pyramids

The volume of a Pyramid can be found by the following formula: \frac{1}{3} A h

  • A = area of base, h = height from base to apex

The surface area of a Pyramid can be found by the following formula:A = A_b + \frac{ps}{2}

  • A = Surface area, Ab = Area of the Base, p = Perimeter of the base, s = slant height.

[edit] Cylinders

The volume of a Cylinder can be found by the following formula: \pi r^2 \cdot h

  • 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: 2 \pi r\ (r+h)

  • r\, is the radius of the circular base, and h\, is the height

[edit] Cones

The volume of a Cone can be found by the following formula: \frac{1}{3} \pi r^2 h

  • 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: \pi\ r (r + \sqrt {r^2 + h^2})

  • r\, is the radius of the circular base, and h\, is the height.

[edit] Spheres

The volume of a Sphere can be found by the following formula: \frac{4}{3} \pi r^3

  • r = radius of sphere

The surface area of a Sphere can be found by the following formula: 4 \pi\ r^2

  • r = radius of the sphere

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