Measures and solids · Ages 12–13
Prisms at work: capacity and water levels worksheet
Part of: Prisms
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Prisms at work: capacity and water levels worksheet
Measures and solids · Ages 12–13
Numsprite
numsprite.com
Name:Date:Score:／48
Write each answer in the space. For word problems, show your working and write a sentence answer.
Part A: Working out and filling in (2 marks each)
1.A cuboid tank is 60 cm long, 30 cm wide and 10 cm high inside (1 L = 1000 cm³). At most how many litres of water does it hold?
Answer:
2.A tank has a base area of 200 cm². After 800 cm³ of water is poured in, by how many cm has the water level risen?
Answer:
3.A tank has a base area of 300 cm². After 3600 cm³ of water is poured in, by how many cm has the water level risen?
Answer:
4.A cuboid tank is 50 cm long and 20 cm wide inside, with water 19 cm deep. 2 L more is poured in, none spilling. How deep is the water now, in cm?
Answer:
5.A cuboid tank is 25 cm long and 40 cm wide inside, with water 19 cm deep. 2 L more is poured in, none spilling. How deep is the water now, in cm?
Answer:
6.A cuboid tank 18 cm long and 10 cm wide holds water 20 cm deep. All of it is poured into another, empty tank with a base area of 150 cm². How deep is the water now, in cm?
Answer:
7.A bar of wax is a prism 13 cm long, its cross-section a right-angled triangle with shorter sides 6 cm and 10 cm. It is melted and made into a cuboid candle with a 5 cm × 2 cm rectangle as its cross-section, with nothing lost. How long is the candle?
Answer:
8.A cuboid tank 17 cm long and 20 cm wide holds water 10 cm deep. All of it is poured into another, empty tank with a base area of 200 cm². How deep is the water now, in cm?
Answer:
9.A bar of wax is a prism 27 cm long, its cross-section a right-angled triangle with shorter sides 7 cm and 4 cm. It is melted and made into a cuboid candle with a 3 cm × 2 cm rectangle as its cross-section, with nothing lost. How long is the candle?
Answer:
Part B: Choose, or true or false (2 marks each)
10.How many cm³ is 25 L?
- A. 2500 cm³
- B. 25,000,000 cm³
- C. 25000 cm³
- D. 250 cm³
Choose the right answer
Answer:
11.Pour 1 L of water into an empty tank with a base area of 100 cm², and the water is 1 cm deep.
True or false?
Answer:
12.Pour 5 L of water into an empty tank with a base area of 500 cm², and the water is 100 cm deep.
True or false?
Answer:
Part C: Word problems (4 marks each)
13.A cuboid container 30 cm long and 46 cm wide holds water 5 cm deep. All of it is poured into another, empty cuboid container 30 cm long and 23 cm wide. Find the depth: put the steps in order.
- A. Water = 30 × 46 × 5 = 6900
- B. Depth = 6900 ÷ 690 = 10
- C. New base = 30 × 23 = 690
Write the letters in the right order
Working:
Answer:
14.A cuboid pool 24 m long and 7 m wide is to be filled to a depth of 2 m. The hose pours in 250 L a minute. How many minutes does it take?
Working:
Answer:
15.A cuboid fish tank is 40 cm long and 15 cm wide inside. A pottery ornament of volume 420 cm³ is put in, right under the water, and none spills. By how many cm does the water rise?
Working:
Answer:
16.A cuboid fish tank is 70 cm long and 30 cm wide inside, with water 50 cm deep. How many litres of water are in it?
Working:
Answer:
17.A workshop melts a cuboid block of wax 18 cm long, 16 cm wide and 8 cm high and makes small candles, each a prism whose cross-section is a right-angled triangle with both shorter sides 4 cm, 11 cm long. The wax is cm³, each candle takes cm³, and at most candles can be made.
Fill in each blank
Working:
Answer:
18.A cuboid fish tank is 40 cm long and 16 cm wide inside. A pottery ornament of volume 832 cm³ is put in, right under the water, and none spills. By how many cm does the water rise?
Working:
Answer:
Show the answers and working
Prisms at work: capacity and water levels worksheet: Answers and working
Part A: Working out and filling in
1. 18 L
It holds 60 × 30 × 10 = 18000 cm³ = 18000 ÷ 1000 = 18 L.
2. 4 cm
The water poured in is a prism on the tank's base: rise = volume ÷ base area = 800 ÷ 200 = 4 cm.
3. 12 cm
The water poured in is a prism on the tank's base: rise = volume ÷ base area = 3600 ÷ 300 = 12 cm.
4. 21 cm
2 L = 2000 cm³; the base is 50 × 20 = 1000 cm², so the water rises 2000 ÷ 1000 = 2 cm; now 19 + 2 = 21 cm deep.
5. 21 cm
2 L = 2000 cm³; the base is 25 × 40 = 1000 cm², so the water rises 2000 ÷ 1000 = 2 cm; now 19 + 2 = 21 cm deep.
6. 24 cm
The water's volume stays the same: 18 × 10 × 20 = 3600 cm³; the new depth = 3600 ÷ 150 = 24 cm.
7. 39 cm
Melted and made again, the volume stays: the wax is 6 × 10 ÷ 2 × 13 = 390 cm³. The candle's cross-section is 5 × 2 = 10 cm², so its length = 390 ÷ 10 = 39 cm.
8. 17 cm
The water's volume stays the same: 17 × 20 × 10 = 3400 cm³; the new depth = 3400 ÷ 200 = 17 cm.
9. 63 cm
Melted and made again, the volume stays: the wax is 7 × 4 ÷ 2 × 27 = 378 cm³. The candle's cross-section is 3 × 2 = 6 cm², so its length = 378 ÷ 6 = 63 cm.
Part B: Choose, or true or false
10. C. 25000 cm³
1 L = 1000 cm³, so 25 L = 25 × 1000 = 25000 cm³.
11. False
1 L = 1 × 1000 cm³; depth = volume ÷ base area = 10 cm.
12. False
5 L = 5 × 1000 cm³; depth = volume ÷ base area = 10 cm.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. A → C → B
Poured from one to the other, the water's volume stays the same: 6900 cm³ ÷ the new base 690 cm² = 10 cm.
14. 1344 minutes
The water: 24 × 7 × 2 = 336 m³ = 336000 L (1 m³ = 1000 L); 336000 ÷ 250 = 1344 minutes.
15. 0.7 cm
The ornament's volume equals the water lifted: the base is 40 × 15 = 600 cm², so the rise is 420 ÷ 600 = 0.7 cm.
16. 105 L
The water is 70 × 30 × 50 cm³, ÷ 1000 for litres: 105 L. Or in dm first: 7 × 3 × 5 = 105 dm³ = 105 L.
17. 2304, 88, 26
The wax is 18 × 16 × 8 = 2304 cm³; each candle 4 × 4 ÷ 2 × 11 = 88 cm³; 2304 ÷ 88 isn't whole, and what is left can't make another, so 26 at most.
18. 1.3 cm
The ornament's volume equals the water lifted: the base is 40 × 16 = 640 cm², so the rise is 832 ÷ 640 = 1.3 cm.
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