CSSE-Style Maths Mock 5 (Essex)
CSSE-Style Maths Mock 5 (Essex) continues the Essex Consortium of Selective Schools' pattern of setting multi-step problems inside a real-life story, built around the volume and capacity of cuboid-shaped containers such as tanks, boxes and crates. CSSE questions of this kind often switch units partway through, for example giving one measurement in metres and another in centimetres, so unit conversion is as important as the volume calculation itself.
Method
- Before calculating a cuboid's volume, write down its three dimensions in the same unit; if one is given in a different unit from the others, convert it first.
- Recall the volume of a cuboid as length x width x height, and recall that 1,000 cubic centimetres is equal to 1 litre, since CSSE questions often ask for a capacity answer in litres rather than cubic centimetres.
- For a question about filling or emptying a container at a steady rate, find the total amount involved first, then divide by the rate to find the time, or multiply the rate by the time to find the amount, depending on what is asked.
- Where a container is described as only partly full, for example three-quarters full, work out the volume represented by that fraction before doing anything else with it.
- Watch for CSSE questions that include a detail, such as a container's colour or material, that is not needed for the calculation, and do not let it distract you from the numbers that matter.
- Write your final answer with the correct unit every time, cubic centimetres, cubic metres, litres or millilitres, since a numerically correct but wrongly labelled answer can lose the final mark.
- Sense-check your final answer against the real world; a paddling pool holding 50,000 litres, for example, is obviously too large, and rereading the question usually reveals where a unit conversion went wrong.
Worked example
A fish tank in the shape of a cuboid measures 60 cm long, 30 cm wide and 40 cm tall. It is filled with water to a depth of 25 cm. How many litres of water are in the tank?
- The base of the tank is 60 cm by 30 cm, and the water reaches a depth of 25 cm, not the full 40 cm height, so use 25 cm as the height for this calculation.
- Multiply the three dimensions together to find the volume of water: 60 x 30 x 25.
- Break this down: 60 x 30 = 1,800, then 1,800 x 25 = 45,000, so the volume of water is 45,000 cubic centimetres.
- Convert to litres, using 1,000 cubic centimetres = 1 litre: 45,000 / 1,000 = 45.
- Final answer: there are 45 litres of water in the tank.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1A cuboid box measures 5cm by 4cm by 10cm. What is its volume?Show answer
Answer: 200 cm cubed (5 x 4 x 10 = 200).
Q2How many millilitres are there in 2.5 litres?Show answer
Answer: 2,500 ml.
Q3A water butt holds 80 litres when full. It is currently half full. How many more litres of water does it need to become completely full?Show answer
Answer: 40 litres (half of 80 is 40, and 80 - 40 = 40).
Q4A cuboid-shaped container has a volume of 360 cubic centimetres. Its base is 12cm by 6cm. What is its height?Show answer
Answer: 5cm (the base area is 12 x 6 = 72, and 360 / 72 = 5).
Q5Convert 3.2 metres into centimetres.Show answer
Answer: 320 cm.
Q6A paddling pool is filled at a rate of 15 litres per minute. How many litres are in the pool after 8 minutes?Show answer
Answer: 120 litres (15 x 8 = 120).
Q7A cube has sides of length 6cm. What is its volume?Show answer
Answer: 216 cm cubed (6 x 6 x 6 = 216).
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
A water tank in the shape of a cuboid measures 80cm long, 50cm wide and 60cm tall. It starts empty and is filled using a hose at a rate of 8 litres per minute. How many minutes does it take to fill the tank completely?
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A cuboid-shaped storage box has a length of 1.2 metres, a width of 80cm, and a volume of 0.48 cubic metres. Work out the height of the box, in centimetres, showing how you dealt with the mixed units.
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Free printable worksheet
Want more practice on paper? Download the csse-style maths mock 5 (essex) worksheet pack - 13 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.
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