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jmc

geometry intermediate

Problem

A pyramid with volume 40 cubic inches has a rectangular base. If the length of the base is doubled, the width tripled and the height increased by , what is the volume of the new pyramid, in cubic inches?
Solution
Since the volume of a pyramid is linear in each of length, width, and height (in particular, ), multiplying any of these dimensions by a scalar multiplies the volume by the same scalar. So the new volume is times the old one, or cubic inches.
Final answer
360