how can i describe generally how to find conversion factors involving squares or cubes?

Question

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Answer 1

The conversion factor from km to miles is 0.62 mi/km.  If you want to convert square kilometers (km²) to square miles (mi²), just square the km-to-miles conversion factor, (0.62)² = (0.62)(0.62) = 0.3844mi²/km²; that is, one square kilometer equals 0.3844 square miles.  For cubes, just cube the conversion factor.