Measurement

New Zealand

Level 6 - NCEA Level 1

Lesson

We've already learnt about volume and how to find the volume of different types of solids, including prisms, cylinders, composite solids, pyramids, cones and spheres.

Now let's look at how we can apply these formulae to different situations in the real world.

A jug holding $2$2 L of drinking cordial has been made with $200$200 mL of the cordial concentrate. What is the concentration of the cordial in terms of mL per L.

The formula relating density ($D$`D`), mass ($M$`M`) and volume ($V$`V`) is $D=\frac{M}{V}$`D`=`M``V`.

A file has a density of $7.2$7.2 grams per cubic centimetre. It also has a mass of $100.8$100.8 grams. What is the file’s volume, $V$`V`?

Think: We need to substitute the values in that we know to find the one we don't know.

Do:

$D$D |
$=$= | $\frac{M}{V}$MV |

$7.2$7.2 | $=$= | $\frac{100.8}{V}$100.8V |

$7.2V$7.2V |
$=$= | $100.8$100.8 |

$V$V |
$=$= | $\frac{100.8}{7.2}$100.87.2 |

$=$= | $14$14 $cm^3$cm3 |

Which cordial is stronger (has a higher concentration)?

A) $3L$3`L` of cordial made with $100mL$100`m``L` of concentrate

B) $2L$2`L` of cordial made with $1L$1`L` of concentrate

Think: Cordial is made up of concentrate and water. The stronger cordial will be the one with less water. We need to make the amount of concentrate or the total amount of cordial equivalent in the two options so we can make a meaningful comparison.

Do: I am going to change (A) so it is in terms of $1L$1`L` of concentrate. To do this, I need to multiply both sides by $10$10 because $1000mL=1L$1000`m``L`=1`L`.

$3L/100mL$3L/100mL |
$=$= | $30L/L$30L/L |

This means that $1L$1`L` of concentrate is used to make $30L$30`L` of cordial in (A) and only $2L$2`L` of cordial in B.

So B) $2L$2`L` of cordial made with $1L$1`L` of concentrate is the stronger rate.

The formula relating density $D$`D`, mass $M$`M` and volume $V$`V` is $D=\frac{M}{V}$`D`=`M``V`.

The density of Copper is $8.94$8.94 g/cm^{3}. If a sample of Copper has a volume of $26$26 cm^{3} and a mass of $M$`M` grams, solve for $M$`M`.

Aquarium medication for fish instructs that $6$6mL should be used for every $5$5L of water in the tank. If there are $0.3$0.3g of medication in each mL, what concentration of active medication, in g/L, will result if used according to directions?

Calculate volumes, including prisms, pyramids, cones, and spheres, using formulae

Apply measurement in solving problems