Units of Measure

A model uses the formula $\displaystyle D = \frac{M}{V}$.
$\displaystyle M$ is measured in kilograms (kg) and $\displaystyle V$ is measured in cubic metres (m$\displaystyle ^3$).
Deduce the units of measure for $\displaystyle D$.

A model uses the formula $\displaystyle W = F \times d$.
$\displaystyle F$ is measured in newtons (N) and $\displaystyle d$ is measured in metres (m).
Deduce the units of measure for $\displaystyle W$.

A model uses the formula $\displaystyle E = P \times t$.
$\displaystyle P$ is measured in litres per hour and $\displaystyle t$ is measured in hours.
Deduce the units of measure for $\displaystyle E$.

A tap fills a container at a constant rate.
$\displaystyle 45$ litres flow into the container in $\displaystyle 90$ seconds.
Calculate the rate at which the container fills.
Your answer must include appropriate units.

Van A uses $\displaystyle 14$ litres of fuel on its delivery route.
Van B uses $\displaystyle 21$ litres of fuel on its delivery route.
A manager concludes that Van A has the more efficient engine.
Explain why this conclusion is not valid.

A square patio of side $\displaystyle 3$ metres takes $\displaystyle 2$ hours to lay.
A builder estimates that a square patio of side $\displaystyle 6$ metres will take $\displaystyle 4$ hours, because the length has doubled.
Explain why this estimate is wrong, and calculate a better estimate.

A factory fills cans with a carbonated fruit drink. The cans produced have a volume of 330 millilitres.

The graph below shows the relationship between time, in seconds, and volume of carbonated fruit drink, in millilitres, as a can is filled.

(a) State the type of relationship modelled in the graph.

(b) Determine the rate at which each can is filled with carbonated fruit drink. Your answer must include appropriate units.

The factory can only fill the cans when there are staff present. The machines in the factory can fill 5 cans at the same time.

(c) Estimate how many cans the factory can fill in one week. State any assumptions you have made.