A cuboid tank is 80 cm long, 50 cm wide and 40 cm high inside (1 L = 1000 cm³). At most how many litres of water does it hold?

160 L. It holds 80 × 50 × 40 = 160000 cm³ = 160000 ÷ 1000 = 160 L.

How many cm³ is 28 L? A. 28000 cm³ B. 2800 cm³ C. 28,000,000 cm³ D. 280 cm³ Choose the right answer

A. 28000 cm³. 1 L = 1000 cm³, so 28 L = 28 × 1000 = 28000 cm³.

Prisms & cylinders · Ages 13–14

Prisms and cylinders at work

Rise = volume ÷ base area; 1 L = 1000 cm³.

How to do it

Method

Rise = volume ÷ base area; 1 L = 1000 cm³

600 ÷ 200 = 3 cm

Another way

One cylinder minus another

πR²h − πr²h = π(R² − r²)h

In full

Capacity and volume: 1 mL = 1 cm³, 1 L = 1000 cm³, 1 m³ = 1000 L = 1 000 000 cm³. Put every length in the same unit before working out a volume. Water rising: the volume poured in (or of a thing sunk right under) = base area × the rise in the water level, so the rise = volume ÷ base area. A 600 cm³ stone in a tank with a 200 cm² base lifts the water 600 ÷ 200 = 3 cm. A hollow prism (a pipe, a ring): volume = (outer circle − inner circle) × length = π(R² − r²)h. Or see it as one cylinder minus another, πR²h − πr²h: the same. Prisms on the same base hold volumes in step with their heights: water twice as deep is twice the volume.

Worked examples

Have a go first, then open each one for the answer and the working.

Example 1
A cuboid tank is 80 cm long, 50 cm wide and 40 cm high inside (1 L = 1000 cm³). At most how many litres of water does it hold?
Show the answer and working
Answer: 160 L
It holds 80 × 50 × 40 = 160000 cm³ = 160000 ÷ 1000 = 160 L.
Example 2
How many cm³ is 28 L?
- A. 28000 cm³
- B. 2800 cm³
- C. 28,000,000 cm³
- D. 280 cm³
Choose the right answer
Show the answer and working
Answer: A. 28000 cm³
1 L = 1000 cm³, so 28 L = 28 × 1000 = 28000 cm³.
Example 3
The hollow cylinder in the picture (a length of pipe) has an outer radius of 11 cm and an inner radius of 4 cm, and is 13 cm long. What is the volume of the pipe itself, in terms of π?
Show the answer and working
Answer: 1365 π cm³
The cross-section is a ring: π × 11² − π × 4² = 105π cm²; volume 105π × 13 = 1365π cm³.

Practice questions to try

Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.

1.A tank has a base area of 120 cm². After 480 cm³ of water is poured in, by how many cm has the water level risen?
Answer:
2.How many cm³ is 16 L?
- A. 16,000,000 cm³
- B. 16000 cm³
- C. 1600 cm³
- D. 160 cm³
Choose the right answer
Answer:
3.A cuboid tank is 10 cm long, 40 cm wide and 30 cm high inside (1 L = 1000 cm³). At most how many litres of water does it hold?
Answer:
4.The hollow cylinder in the picture (a length of pipe) has an outer radius of 8 cm and an inner radius of 2 cm, and is 10 cm long. What is the volume of the pipe itself, in terms of π?
Answer:
5.A cuboid tank 12 cm long and 25 cm wide holds water 8 cm deep. All of it is poured into another, empty tank with a base area of 300 cm². How deep is the water now, in cm?
Answer:

All the answers

1. 4 cm
2. B. 16000 cm³
3. 12 L
4. 600 π cm³
5. 8 cm

Free worksheet: Prisms and cylinders at workWorking out, multiple choice and word problems, with answers and working, to print or save as a PDF

VIP practice notes and papers

Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.

Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
Practice paper: Set out in parts like a school paper, marked, with answers and full working

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