Video Transcript
Which of the following is an
appropriate symbol for the unit of a quantity found by multiplying an area by a
length. (a) Meters cubed, (b) meters
squared, (c) meters, (d) meters to the negative one power, (e) meters to the
negative two power.
Recall that units can be multiplied
and divided like regular variables. So when we think about multiplying
an area by a length, the resulting unit will be a unit for area times a unit for
length. Now looking at our answer choices,
they’re all m raised to various powers. m is the symbol for the unit meter. So each of these answer choices is
some power of the base unit meters.
So to find the symbol we are
looking for, we need to express area and length in terms of meters. For starters, we recall that the
meter is a unit for length. For example, a meter stick is so
called because its length is one meter. We now recall that a square meter
or a meter squared is a unit for area.
We actually don’t need to memorize
this fact. We can work it out by thinking
about the area of a rectangle. Meters are appropriate units for
measuring the length of both sides of a rectangle. Now the area of a rectangle is the
product of the length of its two sides. So appropriate units for measuring
the area of a rectangle would be meters squared. This is because the units of a
length measured in meters times a length measured in meters are meters times meters,
which is meters squared.
Going back to our question, when we
multiply an area by a length, we are multiplying meters squared times meters. And meters squared times meters is
meters times meters times meters, which is meters cubed. So an appropriate symbol for the
units of an area times a length is m cubed, which stands for meters cubed or cubic
meter.
