4.3 Calculate using metric units of capacity
You may need to carry out calculations involving capacity. This may require you to convert between metric units, either before you carry out the calculation or at the end.
Example: Party food
You are cooking for a large party. The recipe you are using calls for 600 ml of milk to make enough for four people.
How many litres of milk will you need to make ten times as much?
First you need to multiply the amount in millilitres by 10:
- 600 × 10 = 6 000 ml
However, the question asks for an amount in litres, not millilitres. To convert from millilitres to litres, you need to divide the figure in millilitres by 1 000. So the amount of milk you need in litres is:
- 6 000 ÷ 1 000 = 6 litres
Now try the following activity using the conversion diagram on the previous page to help you answer the questions. Remember to check your answers once you have completed the questions.
Activity 17: Carrying out calculations involving capacity
Calculate the answers to the following problems without using a calculator. You may double-check your answers with a calculator if you need to. Remember to check your answers.
- A nurse has to order enough soup for 100 patients on a ward. Each patient will eat 400 ml of soup. How many litres of soup must the nurse order?
- Twenty people working in a craft workshop have to share the last two-litre bottle of glue. How many millilitres of glue can each person use? What would this be in centilitres?
- Willow buys a two-litre carton of milk. She measures out 350 ml for a sauce, 25 ml for a cake and 100 ml for her toddler’s bedtime drink. How much milk is left in the carton? Express your answer in millilitres.
- Ben is having a party and he wants to make a non-alcoholic cocktail. He has found a recipe which states that he needs 500 ml of cranberry juice, 500 ml of grape juice, 250 ml of orange juice
and 1 litre of sparkling water to serve eight people. There will be 24 people at the party.
How much of each ingredient will he need? Express your answers in litres.
Will an eight-litre drinks dispenser be big enough to hold his non-alcoholic cocktail?
- First you need to work out how much soup you will need in millilitres:
- 100 × 400 = 40 000 ml
To convert from millilitres to litres, you need to divide the figure in millilitres by 1 000. So the amount of milk you need in litres is:
- 40 000 ÷ 1 000 = 40 litres
- First you need to work out how many millilitres are in 2 litres of glue:
- 2 × 1 000 = 2 000 ml
This amount is then divided between the twenty people working in the shop:
- 2 000 ÷ 20 = 100 ml each
To convert this into centilitres, you would divide this answer by 10:
- 100 ÷ 10 = 10 cl each
- First add together the amount of milk Willow has used:
- 350 ml + 25 ml + 100 ml = 475 ml
The carton holds two litres, which in millilitres is:
- 2 litres × 1 000 = 2 000 ml
Now take the amount used away from the amount the carton holds:
- 2 000 ml – 475 ml = 1 525 ml
So 1 525 ml is left in the carton.
The quantities stated are enough to make the drink for eight people. If 24 people are invited to the party, Ben will need three times as much ingredients as stated in the recipe (8 × 3 = 24). So he will need:
500 ml × 3 = 1 500 ml of cranberry juice (1 500 ÷ 1 000 = 1.5 litres)
500 ml × 3 = 1 500 ml of grape juice (1 500 ÷ 1 000 = 1.5 litres)
250 ml × 3 = 750 ml of orange juice (750 ÷ 1 000 = 0.75 litres)
1 litre × 3 = 3 litres of sparkling water (this is already in litres, so no conversion is needed)
To see if the bowl will be big enough, we need to add the quantities expressed in litres together:
- 1.5 litres + 1.5 litres + 0.75 litres + 3 litres = 6.75 litres
So the eight-litre drinks dispenser will be big enough.
In this section you have learned how to:
- identify the standard units for measuring volume or capacity
- measure volumes
- convert between metric units of capacity
- carry out calculations with metric units of capacity.