Capacity

To celebrate the end of term, the Year 7 students have bought several bottles of orange juice. If each bottle has a capacity of $1.5\ L$, express this amount in centiliters ($cL$) and in milliliters ($mL$).

Match each of the following objects with the unit of capacity of the metric system that you think is most suitable for measuring what fits inside it:

• An Olympic swimming pool.

• A can of cola.

• A syringe for giving a vaccine.

• A mop bucket.

Complete the following statements by converting to the required units:

1. a) $25 L = ??? dL$
2. b) $4,500 mL = ??? L$
3. c) $0.75 kL = ??? L$
4. d) $32 cL = ??? mL$

An athlete carries a hydration pack for her training. If she has filled the reservoir with $1,200\ mL$ of water and then added an extra bottle of $0.5\ L$, how many liters of water does she carry in total?

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

A farmer has a small tank to water his pots, with a capacity of $2\ dal$ and $5\ L$. How many $1\ L$ bottles can he fill when the tank is completely full?

A recipe for a sponge cake states that you need to add $2\ dL$ of milk. 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.

At a music festival for teenagers, the organisers have bought several types of water containers to distribute among 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, carry out the following conversions:

1. a) Express the capacity of the tank in liters.
2. b) How many liters are 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?

Order the following measurements of capacity from smallest to largest. To compare them, first convert them all to 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 is in 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 needed to fill it?

An aquarium in the shape of a rectangular prism has interior dimensions of $80\text{ cm}$ long, $30\text{ cm}$ wide and $50\text{ cm}$ high. For safety reasons, 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 needed to reach the recommended maximum level?

In the science lab, the students are preparing a mixture for an experiment on density. They have used the following amounts 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 amount of the mixture in simple form in centiliters ($cl$) and then in compound form using liters, deciliters, and milliliters.

A group of friends is going on a mountain hike. Each of them carries a backpack with a water bladder (camelbak). If the mass of one liter of water is approximately $1\text{ kg}$:

1. a) If Marcos's water bladder has a capacity of $2,500\text{ ml}$, how many kilograms does the water add to the weight of his backpack when full?
2. b) Lucía carries a $75\text{ cl}$ bottle. If she has already drunk one third of the contents, how many grams of water does she have left?
3. c) How many bottles like Lucía's ($75\text{ cl}$) could be filled with the water from a $1.5\text{ dal}$ drum?

For a birthday party, a teenager decides to make a homemade "fruit punch" by mixing the following ingredients:

• $2$ bottles of orange soda of $1.5\text{ L}$ each.

• $3$ cartons of pineapple juice of $33\text{ cl}$ each.

• $1$ bottle of lemonade of $2\text{ L}$.

• $250\text{ ml}$ of strawberry syrup.

1. a) How many liters of punch will they get in total?
2. b) If they want to serve the punch in $200\text{ ml}$ glasses, how many full glasses can they fill?
3. c) Will there be any punch left over? If so, express the leftover amount in centiliters.

A garden swimming pool has a total capacity of $12\text{ m}^3$. We want to fill it using a hose delivering 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 time above in hours and minutes.

A perfume factory wants 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.

• One 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 faulty faucet in a high school drips one drop of water every $2\text{ seconds}$. If each drop has an average volume of $50\text{ mm}^3$, calculate how many $2\text{ decaliters}$ drums would be filled if the faucet leaked water continuously throughout the month of April.

A farmer has an irrigation tank containing a compound volume of $2\text{ kl}$, $5\text{ hl}$ and $8\text{ dal}$ of water. To fertilize his trees, he must mix the water with a liquid fertilizer in a ratio of $15\text{ ml}$ of fertilizer for every liter of water. If he has $5\text{ liters}$ bottles of fertilizer, how many full bottles will he need to buy to use all the water in the tank? Will there be any fertilizer left over in the last bottle? Express the leftover amount in centiliters.

A tanker truck carries $12.5\text{ m}^3$ of milk. Upon arrival at the processing plant, the contents are unloaded into three different tanks:

1. $4,500\text{ liters}$ is unloaded into the first tank.

2. $52\text{ hectoliters}$ is unloaded into the second tank.

3. The rest is divided equally into $200$ industrial containers.

What is the capacity of each of those $200$ containers expressed in $dm^3$?

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 $\text{RD\$}\ 4.50$.

• Container B: $0.25\text{ dal}$ at a price of $\text{RD\$}\ 6.50$.

Calculate the price per liter for each container and determine which is cheaper. If a family uses $15\text{ cl}$ of detergent per wash, how many washes can they do with the larger container?

A laboratory experiment requires filling a graduated cylinder with three immiscible liquids:

1. $0.045\text{ dm}^3$ of mercury.

2. $12.5\text{ centiliters}$ of distilled water.

3. $850\text{ cubic millimeters}$ of oil.

What will be the total volume of the mixture in the graduated cylinder expressed in compound form (using liters, deciliters, and milliliters)? Note: Remember that $1\text{ ml} = 1\text{ cm}^3$.

A local council 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 through evaporation in a single day?
2. b) If water costs $\text{RD\$}\ 1.20$ per cubic meter ($m^3$), how much money does the water loss cost the council after a week of intense heat?