Capacity in the Metric System

Match each of the following objects with the unit of capacity in the Metric System that seems most appropriate to measure what fits inside it:

• An Olympic swimming pool.

• A can of cola.

• A syringe for giving a vaccine.

• A mop bucket.

Complete the following equalities by performing the necessary unit conversions:

1. a) $25 L = ??? dL$
2. b) $4.500 mL = ??? L$
3. c) $0,75 kL = ??? L$
4. d) $32 cL = ??? mL$

To celebrate the end of the term, the 7th grade students have bought several bottles of orange juice. If each bottle has a capacity of $1,5\ L$, express this quantity in centiliters ($cL$) and in milliliters ($mL$).

At a music festival for teenagers, the organizers have bought several types of water containers to distribute among the attendees. They have a main tank of $2,5\text{ kL}$, packs of bottles of $50\text{ cl}$, and large bottles of $8\text{ L}$.

If they want to know the total water available in liters, perform the following conversions:

1. a) Express the capacity of the tank in liters.
2. b) How many liters are there in a pack containing $12$ bottles of $50\text{ cl}$?
3. c) If they have served $15$ full large bottles, how many deciliters have they distributed?

In Science class, the students are using a graduated cylinder. If the cylinder shows a capacity of $35\ cL$, express this measurement in complex form (that is, using liters and centiliters).

A farmer has a small tank for watering his pots with a capacity of $2\ dal$ and $5\ L$. How many $1\ L$ bottles will he be able to fill with the tank completely full?

In the Natural Sciences laboratory, the students are preparing a mixture for an experiment on density. They have used the following quantities of different liquids:

• Distilled water: $1\text{ L}$ and $25\text{ cl}$.

• Alcohol: $4\text{ dl}$ and $5\text{ ml}$.

• Oil: $150\text{ ml}$.

Express the total quantity of the mixture in incomplex form in centiliters ($cl$) and then in complex form using liters, deciliters, and milliliters.

An athlete carries a hydration backpack for her training. If she has filled the tank with $1.200\ mL$ of water and then added an extra $0,5\ L$ bottle, how many liters of water is she carrying in total?

A recipe for making a sponge cake indicates that $2\ dL$ of milk must be added. If we have an open one-liter carton in the fridge with $450\ mL$ left, do we have enough milk for the recipe? Justify your answer by converting both quantities to the same unit.

Order the following capacity measurements from smallest to largest. To be able to compare them, first convert them all to the unit of liters ($L$):

• $0,007\text{ kL}$

• $75\text{ dl}$

• $725\text{ cl}$

• $7.100\text{ ml}$

• $0,8\text{ dal}$

Remember that in the metric system there is a direct relationship between volume and capacity. If we have a cube-shaped container that has a volume of exactly $1\ dm^3$, how many liters of water fit inside it? And how many milliliters fit in a volume of $1\ cm^3$?

An aquarium has the shape of a cuboid (rectangular prism) with the dimensions shown in the image. Knowing that $1\text{ dm}^3$ is exactly equivalent to $1\text{ liter}$ of capacity:

1. a) Calculate the volume of the aquarium in $\text{dm}^3$.
2. b) How many liters of water are needed to fill the aquarium completely?
3. c) If the aquarium currently contains $45.000\text{ ml}$ of water, how many liters are left to fill it?

An aquarium in the shape of a rectangular prism has internal dimensions of $80\text{ cm}$ long, $30\text{ cm}$ wide, and $50\text{ cm}$ high. For safety, it is recommended not to fill it to more than $\frac{4}{5}$ of its total capacity. If it currently contains $84\text{ liters}$ of water, how many $250\text{ cl}$ buckets are left to pour in to reach the maximum recommended level?

A garden swimming pool has a total capacity of $12\text{ m}^3$. We want to fill it using a hose that delivers a flow rate of $25\text{ liters}$ per minute.

1. a) How many liters of water fit in the pool? (Remember that $1\text{ m}^3 = 1.000\text{ L}$).
2. b) How many minutes will it take to fill the pool completely?
3. c) Express the previous time in hours and minutes.

In a perfume factory, they want to bottle a batch of $0,15\text{ m}^3$ of lavender essence. Three types of bottles are used:

• Half of the essence is bottled in $125\text{ ml}$ bottles.

• A third of the total is bottled in $0,5\text{ dl}$ bottles.

• The rest of the essence is bottled in $10\text{ cm}^3$ samples.

Calculate how many bottles of each type are needed.

A municipal swimming pool $25\text{ m}$ long and $12\text{ m}$ wide is filled to an average depth of $1,8\text{ meters}$. Due to evaporation from the heat, the water level drops by $5\text{ mm}$ each day.

1. a) How many liters of water are lost to evaporation in a single day?
2. b) If water costs $\$1,20\text{ \$}$ per cubic meter ($m^3$), how much money does the loss of water cost the city council after a week of intense heat?

A faulty tap leaks water at a rate of $15\text{ gotas}$ per minute. If each drop has a volume of approximately $0,05\text{ ml}$:

1. a) How many milliliters of water are lost in an hour?
2. b) How many liters of water will have been wasted after a full day ($24$ hours)?
3. c) If water costs $0,002\text{ \$}$ per liter, how many dollars are lost in a month of $30$ days due to this leak?

We want to compare the value for money of two containers of liquid detergent of the same brand:

• Container A: $1.800\text{ ml}$ at a price of $4,50\text{ \$}$.

• Container B: $0,25\text{ dal}$ at a price of $6,50\text{ \$}$.

Calculate the price per liter of each container and determine which is more economical. If a family consumes $15\text{ cl}$ of detergent in each wash, how many washes can they do with the largest container?

A broken faucet in a middle school leaks one drop of water every $2\text{ seconds}$. If each drop has an average volume of $50\text{ mm}^3$, calculate how many $2\text{ decaliters}$ containers would be filled if the faucet were leaking water throughout the whole month of April.