text: The calculation of this quantity is the most straightforward result of a triple integral of just a Jacobian [YAH-koh-bee-un].
full_question: The calculation of this quantity is the most straightforward result of a triple integral of just a Jacobian [YAH-koh-bee-un]. For a parallelepiped [“parallel-uh-PIE”-ped], this quantity is found using a triple product. The derivative of this quantity with respect to radius gives the surface area of a sphere. The factor this value changes by during a transformation can be calculated by taking the determinant of a 3-by-3 matrix. For a cone or pyramid, this quantity equals one-third times height times base area. Name this measurement of the space taken up by a three-dimensional object.
first_sentence: The calculation of this quantity is the most straightforward result of a triple integral of just a Jacobian [YAH-koh-bee-un].