Volume and Capacity of Cuboids
The volume of a cuboid is the amount of three-dimensional space it occupies, found by multiplying length x width x height. Capacity measures how much liquid a container can hold, and for practical problems 1 cm^3 of volume is equivalent to 1 ml of capacity, with 1000 cm^3 equal to 1000 ml, or 1 litre. 11+ papers combine cuboid volume with capacity conversions, finding a missing dimension from a known volume, and combining or comparing containers.
Before you start
Make sure you're comfortable with these topics first:
Method
- Recall the volume formula for a cuboid, V = length x width x height, making sure every measurement uses the same unit before multiplying.
- Learn the link between volume and capacity: 1 cm^3 = 1 ml, and 1000 cm^3 = 1000 ml = 1 litre, so a volume in cm^3 converts directly to a capacity in ml.
- To find a missing dimension when the volume is already known, divide the volume by the product of the two given dimensions.
- For a composite solid made of two cuboids joined together, find the volume of each cuboid separately, then add them.
- For 'how many smaller containers fill a larger one' problems, divide the larger volume or capacity by the smaller one, and interpret any remainder in context, such as a partly-filled extra container.
- Always check your final units match what the question asks for (cm^3, litres or ml), and convert if they do not.
Worked example
A fish tank is a cuboid 40 cm long, 25 cm wide and 30 cm tall. (a) Calculate its volume in cm^3. (b) The tank is completely filled with water. How many litres of water does it hold?
- Multiply the three dimensions to find the volume: 40 x 25 x 30.
- 40 x 25 = 1000, then 1000 x 30 = 30,000 cm^3. This is the answer to (a).
- Convert cm^3 to litres using 1000 cm^3 = 1 litre, so divide by 1000.
- 30,000 / 1000 = 30 litres. This is the answer to (b).
- Check the answer is sensible: a fish tank of this size holding 30 litres is a realistic size for a classroom aquarium.
Practice questions
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Q1Calculate the volume of a cuboid measuring 6 cm by 5 cm by 4 cm.Show answer
Answer: 120 cm^3 (6 x 5 x 4)
Q2A cuboid has a volume of 200 cm^3, and its base is 10 cm by 5 cm. Find its height.Show answer
Answer: 4 cm (200 / (10 x 5))
Q3Convert 4,500 cm^3 into litres.Show answer
Answer: 4.5 litres (4,500 / 1000)
Q4A carton holds 750 ml of juice. How many cm^3 is this?Show answer
Answer: 750 cm^3 (since 1 ml = 1 cm^3)
Q5A tank holds 5 litres of water. How many cm^3 is this?Show answer
Answer: 5,000 cm^3 (5 x 1000)
Q6A box is a cube with edges of 8 cm. Calculate its volume.Show answer
Answer: 512 cm^3 (8 x 8 x 8)
Q7A shape is made of two cuboids joined together: one measuring 4 cm by 3 cm by 2 cm, and another measuring 5 cm by 3 cm by 2 cm. Find the total volume.Show answer
Answer: 54 cm^3 ((4x3x2) + (5x3x2) = 24 + 30)
Q8A jug holds 1.2 litres. How many 150 ml glasses can be completely filled from a full jug?Show answer
Answer: 8 glasses (1,200 / 150)
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
A cuboid-shaped box has a volume of 360 cm^3. Its length is 10 cm and its width is 6 cm. Calculate its height, and state the capacity of the box in millilitres.
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A water tank is a cuboid measuring 50 cm by 40 cm by 60 cm. It is currently filled with water to a depth of 25 cm. (a) How many litres of water are currently in the tank? (b) How many more litres are needed to fill the tank completely?
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Free printable worksheet
Want more practice on paper? Download the volume and capacity of cuboids worksheet pack - 4 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 31 of 11+ Maths Workbook 2, the whole course as one free printable PDF.
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