Video Transcript
True or false: A cylinder with a
volume of one sixtieth of a cubic meter and a mass of 150 kilograms has a density of
9,000 kilograms per cubic meter.
We recall that the density of any
object is equal to its mass divided by its volume. If the mass is measured in
kilograms and the volume in cubic meters, then the units for density will be
kilograms per cubic meter. In this question, we are told the
cylinder has a mass of 150 kilograms and a volume of one sixtieth of a cubic
meter. The density will therefore be equal
to 150 divided by one sixtieth. Dividing by a fraction is the same
as multiplying by the reciprocal of the fraction. This is sometimes known as KCF. We keep the first number the same,
we change the sign to a multiplication, and we flip the fraction.
60 divided by one is equal to
60. So the density is equal to 150
multiplied by 60. 15 multiplied by six is equal to
90. This means that 150 multiplied by
60 is equal to 9,000. The density of the cylinder is
9,000 kilograms per cubic meter. As this is the value we were given
in the statement, the correct answer is true. A cylinder with a volume of one
sixtieth of a cubic meter and a mass of 150 kilograms will have a density of 9,000
kilograms per cubic meter.
