Exercises: Capacity

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 ($mL$).

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) $32 cL = ??? mL$

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?

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?

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 $1\ cm^3$?

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.

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 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 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?

A group of friends goes on a hiking trip to the mountains. Each carries a backpack with a hydration pack (camelbak). If the weight of one liter of water is approximately $1\text{ kg}$:

1. a) If Mark's hydration pack has a capacity of $2.500\text{ ml}$, how many kilos does the water add to the weight of his backpack when it is full?
2. b) Lucy carries a $75\text{ cl}$ bottle. If she has already drunk a third of the contents, how many grams of water does she have left?
3. c) How many bottles like Lucy's ($75\text{ cl}$) could be filled with the water from a $1,5\text{ dal}$ container?

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

• $0,007\text{ kL}$

• $75\text{ dl}$

• $725\text{ cl}$

• $7.100\text{ ml}$

• $0,8\text{ dal}$

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?

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

• $2$ bottles of orange soft drink 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 he get in total?
2. b) If he wants to serve the punch in $200\text{ ml}$ glasses, how many glasses will he be able to fill completely?
3. c) Will he have any punch left over? If so, express the remainder in centiliters.

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.

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?

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 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.

A farmer has an irrigation tank containing a complex form 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 proportion of $15\text{ ml}$ of fertilizer for every liter of water. If he has $5\text{ liters}$ containers of fertilizer, how many full containers must he buy to use all the water in the tank? Will there be any fertilizer left over in the last container? Express the remainder in centiliters.

A tanker truck transports $12,5\text{ m}^3$ of milk. Upon arriving at the processing plant, the contents are unloaded into three different tanks:

1. $4.500\text{ liters}$ are unloaded into the first tank.

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

3. The rest is distributed 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 $4,50\text{ \$}$.

• 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 laboratory experiment requires filling a graduated cylinder with three liquids that do not mix:

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 cylinder expressed in complex form (using the units of liters, deciliters, and milliliters)? Note: Remember that $1\text{ ml} = 1\text{ cm}^3$.

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?