This mixed practice stop brings together 1 topics from Primary 6 Volume: Mixed practice. Nothing on the question says which topic it comes from, so choosing the method is part of the skill. In the lesson. Cubic centimetres means a volume, square centimetres means a floor area, and centimetres means a side.
Lesson video, with the working
Volume mixed-practice questions
2 min 38 s
The film teaches 1 question. The question shows first; its working is written as the film explains it.
A tank with a square base is 20 cm high. It contains 2.7 ℓ of water, and the water stands 12 cm deep. Find the length of one side of the base.
One side of the base is 15 cm.
Ans: 15 cm
How to solve it
Convert first so the units match: 2.7 litres is two thousand, seven hundred millilitres, and 1 millilitre is 1 cubic centimetre.
Use the water's own depth, 12 centimetres, as the height, not the tank's 20 centimetres.
Divide the volume by the depth to get the floor: two thousand, seven hundred divided by 12 is 225 square centimetres.
The base is a square, so one side is the square root of 225.
15 times 15 is 225, so one side of the base is 15 centimetres.
The side of a square base is the square root of its area. Cubic centimetres means a volume, square centimetres means a floor area, and centimetres means a side.
Practice questions with worked solutions
Question 1 is free to try. The other question opens in the free trial, each with its full working.
Question 1 of 2 · Challenge · free to tryA tank with a square base is 16 cm high. It contains 1.8 ℓ of water, and the…A tank with a square base is…
A tank with a square base is 16 cm high. It contains 1.8 ℓ of water, and the water stands 8 cm deep. (a) Find the length of one side of the base. (b) How many more millilitres of water are needed to fill the tank to the brim?
Work it out on paper, then open the working and check your answer against it.
conversion fact = unit relation for 1 ℓ = 1000 ml = 1000 cm³
water volume in cubic centimetres = converted value of 1.8 ℓ = 1800 ml = 1800 cm³
base area = 1800 ÷ 8 = 225
side = √225 = 15 cm
capacity = 225 × 16 = 3600
more water = 3600 − 1800 = 1800
Answer: side 15 cm, 1800 ml more
For parents
How do you solve P6 volume mixed practice questions?
These questions chain several volume steps together, often in two parts: convert litres, find a base area from a volume and a water depth, find a side, then a capacity.
What your child learns here
These questions chain several volume steps together, often in two parts: convert litres, find a base area from a volume and a water depth, find a side, then a capacity. They draw on the Primary 6 Volume of Cube and Cuboid outcomes together with the link between litres and cubic centimetres.
Convert litres or millilitres to cubic centimetres before any division.
Divide a volume of water by the water's depth to get the base area.
Find the side of a square base as the square root of its area.
Find a tank's capacity from its base area and full height, then the water still needed.
Does the answer make sense?
A side of the square base must come out much smaller than the base area it came from, since side times side gives that area. The water your child says is still needed, plus the water already there, must make the whole capacity, and a layered solid holds fewer cubes than its full box.
How to practise these questions
This set mixes the Volume chapter's question types. Intermediate questions chain unit changes with volume, area and length in a single question. Challenge questions chain capacity and length further, finding a side of the tank first and then how much more water fills it to the brim. If a mixed volume question stalls, read the written step-by-step solution.
Questions parents ask
Why are volume questions split into parts (a) and (b)? Each part builds on the one before. In a tank question, an early part might find a base area, and a later part use it to find a capacity.
How do you convert litres to cubic centimetres? Multiply by 1000. One litre is 1000 millilitres, and one millilitre is one cubic centimetre, so 2.4 litres is 2400 cubic centimetres.
Is P6 volume practice available? Yes. Question 1 on this page is free with its working, and members can practise every mixed volume question with a worked solution.
