Prisms · Ages 12–13
Prisms at work: capacity and water levels
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
Volume in step with depth
depth × 2 → volume × 2
In full
Capacity and volume: 1 mL = 1 cm³, 1 L = 1000 cm³, 1 m³ = 1000 L. Put every length in the same unit before working out a volume. A tank is a prism (most often a cuboid): the water's volume = base area × depth. 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. Poured into another container, the water keeps its volume: the new depth = volume ÷ the new base area. A prism melted down and cast into another shape keeps its volume too. Another way to see it: 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
How many cm³ is 15 L?
- A. 150 cm³
- B. 1500 cm³
- C. 15,000,000 cm³
- D. 15000 cm³
Choose the right answer
Show the answer and working
Answer: D. 15000 cm³
1 L = 1000 cm³, so 15 L = 15 × 1000 = 15000 cm³.
Example 2
A cuboid tank is 40 cm long and 25 cm wide inside, with water 16 cm deep. 2 L more is poured in, none spilling. How deep is the water now, in cm?
Show the answer and working
Answer: 18 cm
2 L = 2000 cm³; the base is 40 × 25 = 1000 cm², so the water rises 2000 ÷ 1000 = 2 cm; now 16 + 2 = 18 cm deep.
Example 3
A cuboid tank 15 cm long and 28 cm wide holds water 10 cm deep. All of it is poured into another, empty tank with a base area of 100 cm². How deep is the water now, in cm?
Show the answer and working
Answer: 42 cm
The water's volume stays the same: 15 × 28 × 10 = 4200 cm³; the new depth = 4200 ÷ 100 = 42 cm.
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.How many cm³ is 17 L?
- A. 170 cm³
- B. 17,000,000 cm³
- C. 17000 cm³
- D. 1700 cm³
Choose the right answer
Answer:
2.A tank has a base area of 500 cm². After 2500 cm³ of water is poured in, by how many cm has the water level risen?
Answer:
3.Pour 4 L of water into an empty tank with a base area of 500 cm², and the water is 0.8 cm deep.
True or false?
Answer:
4.A cuboid tank 25 cm long and 12 cm wide holds water 18 cm deep. All of it is poured into another, empty tank with a base area of 600 cm². How deep is the water now, in cm?
Answer:
5.A bar of wax is a prism 19 cm long, its cross-section a right-angled triangle with shorter sides 4 cm and 12 cm. It is melted and made into a cuboid candle with a 4 cm × 3 cm rectangle as its cross-section, with nothing lost. How long is the candle?
Answer:
All the answers
- 1. C. 17000 cm³
- 2. 5 cm
- 3. False
- 4. 9 cm
- 5. 38 cm
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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