Volume

  • The volume of an object is a three-dimensional measurement of the space it occupies. The formulae for the volume $ V $ of common shapes are:

    shapeformulanote
    cube$  V = a^3^ $where $ a $ is the length of the sides
    sphere$  V = (4/3) \pi r^3^  $where $ r $ is the radius
    cylinder$  V = \pi r^2^ $ $ h $where $ r $ is the radius and $ h $ is the height
    general$  V = \int A(h) dh  $where $ h $ is the height and $ A(h) $ is the area of a cross-section perpendicular to $ h $ as a function of $ h $

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