### Video Transcript

The density of lead is 11.34 grams
per centimetre cubed. Given that one kilogram is equal to
2.2 pounds and one centimetre equals 0.4 inches, calculate the density of lead in
pounds per cubic inch.

Before starting this problem, it is
worth remembering the formula density is equal to mass divided by volume. The density of lead in the question
was given in grams per centimetre cubed. This is because mass can be
measured in grams and volume in centimetres cubed.

We want to convert this into pounds
per cubic inch. This can be written using the same
notation as grams per centimetre cubed. The mass can be measured in pounds
and the volume in inches cubed. In this case, we’re converting from
metric units to imperial units. We need to convert 11.34 grams per
centimetre cubed into pounds per inch cubed.

We were told in the question the
conversion that one kilogram is equal to 2.2 pounds. As there are 1000 grams in one
kilogram, then 1000 grams must also be equal to 2.2 pounds. We now need to scale this
conversion to calculate how many pounds are in 11.34 grams.

Dividing both sides by 1000 shows
us that one gram is equal to 0.0022 pounds. Multiplying the left-hand side by
11.34 gives us 11.34 grams. And multiplying the left-hand side
by 11.34 gives us 0.024948. Therefore, 11.34 grams is equal to
0.024948 pounds.

We now need to consider the
volume. Once again, we were told in the
question that one centimetre is equal to 0.4 inches. As this is a measure of length, we
need to cube both sides to get a measure of volume, as volume is measured in
centimetres cubed or inches cubed. One cubed is equal to one, and 0.4
cubed is equal to 0.064. Therefore, one centimetre cubed is
equal to 0.064 inches cubed.

We can therefore say that 11.34
grams per centimetre cubed is equal to 0.024948 pounds per 0.064 inches cubed. We want to calculate the density in
pounds per cubic inch or per inch cubed. Therefore, we need to divide both
sides by 0.064. 0.024948 divided by 0.064 is equal
to 0.3898125. This means that the density of lead
is 0.3898125 pounds per inch cubed or per cubic inch.

It would be sensible to round this
to two decimal places. The nine is the deciding
number. And as this is bigger than five, we
round up. The density of lead to two decimal
places is 0.39 pounds per cubic inch.