# Geometry/Chapter 9

## Contents

## 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.

In the following formula, V=volume, A=base area, and h=height.

<math>V=Ah</math>

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:

- <math>SA = 2lw + 2lh + 2wh</math>
- where
*l*= length of the base,*w*= width of the base,*h*= height

- where

## Pyramids

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

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

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

- <math>A</math> = Surface area, <math>A_b</math> = Area of the Base, <math>p</math> = Perimeter of the base, <math>s</math> = slant height.

## Cylinders

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

*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: <math>2 \pi r\ (r+h) </math>

- <math>r\,</math> is the radius of the circular base, and <math>h\,</math> is the height

## Cones

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

*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: <math>\pi\ r (r + \sqrt {r^2 + h^2})</math>

- <math>r\,</math> is the radius of the circular base, and <math>h\,</math> is the height.

## Spheres

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

*r*= radius of sphere

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

*r*= radius of the sphere

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