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# 3D Shapes

### Surface areas and volume of 3D shapes

Term | Definition |
---|---|

2πr | circumference of a circle |

1/2 d1d2 | area of a rhombus |

πr² | area of a circle |

s² | area of a square |

1/2 ap | area of a regular polygon |

h(b1+b2)/2 | area of a trapezoid |

Ph | lateral area of prism |

La+2B | Total area of a prism |

Bh | volume of prism |

6e² | total area of a cube |

e³ | volume of a cube |

1/2 Pl | surface area of a pyramid |

LA+B | total area of a pyramid |

1/3 Bh | volume of a pyramid |

Ch | Lateral area of cylinder |

LA+2B | Total Area of a cylinder |

Bh | volume of cylinder |

1/2Cl | Lateral Area of a Cone |

LA+B | total area of a cone |

1/3Bh | volume of a cone |

4/3 πr³ | volume of a sphere |

a²+h²=l² | slant height |

Cube | SA = 6(e squared) V = e cubed |

Rectangular Prism | SA = 2(lw + wh + lh) V = Bh |

Prism | SA = Sum of the Area of the Bases OR Perimeter of the base times the height + area of two bases V = Bh |

Cylinder | SA = 2pi(radius squared) + 2pi(rh) V = pir squaredh |

Pyramid | SA = Sum of the areas of the faces V = 1/3 Bh |

Cone | SA = pi*r (l+r) V = 1/3 pir squaredh |

Sphere | SA = 4pir squared V = 4/3 pi*r cubed |