Measures and solids · Ages 13–14

Prisms and cylinders at work worksheet

Part of: Prisms & cylinders

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Measures and solids · Ages 13–14

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Write each answer in the space. For word problems, show your working and write a sentence answer.

1.A tank has a base area of 250 cm². After 2750 cm³ of water is poured in, by how many cm has the water level risen?
Answer:
2.A cuboid tank is 40 cm long, 60 cm wide and 40 cm high inside (1 L = 1000 cm³). At most how many litres of water does it hold?
Answer:
3.The hollow cylinder in the picture (a length of pipe) has an outer radius of 9 cm and an inner radius of 6 cm, and is 39 cm long. What is the volume of the pipe itself, in terms of π?
Answer:
4.The cylindrical container in the picture has a base radius of 8 cm and water 12 cm deep. A stone is dropped in and sinks right under, and the water rises 1 cm. What is the stone's volume, in terms of π?
Answer:
5.The hollow cylinder in the picture (a length of pipe) has an outer radius of 9 cm and an inner radius of 2 cm, and is 11 cm long. What is the volume of the pipe itself, in terms of π?
Answer:
6.A cuboid tank 15 cm long and 17 cm wide holds water 20 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:
7.Take π as 3.14. 1256 mL of water is poured into an empty cylindrical cup of base radius 10 cm. How deep is the water, in cm?
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8.A cuboid tank 15 cm long and 30 cm wide holds water 15 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:

9.How many cm³ is 2 L?
- A. 2000 cm³
- B. 2,000,000 cm³
- C. 20 cm³
- D. 200 cm³
Choose the right answer
Answer:
10.How many cm³ is 7 L?
- A. 7,000,000 cm³
- B. 700 cm³
- C. 70 cm³
- D. 7000 cm³
Choose the right answer
Answer:
11.Pour 1 L of water into an empty tank with a base area of 500 cm², and the water is 0.2 cm deep.
True or false?
Answer:
12.Pour 3 L of water into an empty tank with a base area of 500 cm², and the water is 0.6 cm deep.
True or false?
Answer:

13.A cuboid container 37 cm long and 24 cm wide holds water 11 cm deep. All of it is poured into another, empty cuboid container 37 cm long and 33 cm wide. Find the depth: put the steps in order.
- A. New base = 37 × 33 = 1221
- B. Depth = 9768 ÷ 1221 = 8
- C. Water = 37 × 24 × 11 = 9768
Write the letters in the right order
Working:
Answer:
14.A cuboid pool 16 m long and 12 m wide is to be filled to a depth of 2 m. The hose pours in 500 L a minute. How many minutes does it take?
Working:
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15.A cylindrical flask is 5 cm in base radius and 13 cm high inside. Its capacity in terms of π is π cm³; taking π as 3.14, it holds about mL of hot water.
Fill in each blank
Working:
Answer:
16.A cuboid fish tank is 50 cm long and 30 cm wide inside. A pottery ornament of volume 2250 cm³ is put in, right under the water, and none spills. By how many cm does the water rise?
Working:
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17.A cuboid fish tank is 30 cm long and 40 cm wide inside, with water 40 cm deep. How many litres of water are in it?
Working:
Answer:
18.A concrete pipe is 2 m long, with an outer radius of 40 cm and an inner radius of 25 cm (take π as 3.14). How many m³ of concrete does it take?
Working:
Answer:

Show the answers and working

Prisms and cylinders at work worksheet: Answers and working

1. 11 cm
The water poured in is a prism on the tank's base: rise = volume ÷ base area = 2750 ÷ 250 = 11 cm.
2. 96 L
It holds 40 × 60 × 40 = 96000 cm³ = 96000 ÷ 1000 = 96 L.
3. 1755 π cm³
The cross-section is a ring: π × 9² − π × 6² = 45π cm²; volume 45π × 39 = 1755π cm³.
4. 64 π cm³
The stone's volume equals the water it lifts: base area π × 8² = 64π, times the 1 cm rise: 64π cm³. The water's first depth isn't needed.
5. 847 π cm³
The cross-section is a ring: π × 9² − π × 2² = 77π cm²; volume 77π × 11 = 847π cm³.
6. 17 cm
The water's volume stays the same: 15 × 17 × 20 = 5100 cm³; the new depth = 5100 ÷ 300 = 17 cm.
7. 4 cm
1256 mL = 1256 cm³; the base is 3.14 × 10² = 314 cm², so the depth is 1256 ÷ 314 = 4 cm.
8. 45 cm
The water's volume stays the same: 15 × 30 × 15 = 6750 cm³; the new depth = 6750 ÷ 150 = 45 cm.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. C → A → B
Poured from one to the other, the water's volume stays the same: 9768 cm³ ÷ the new base 1221 cm² = 8 cm.
14. 768 minutes
The water: 16 × 12 × 2 = 384 m³ = 384000 L (1 m³ = 1000 L); 384000 ÷ 500 = 768 minutes.
15. 325, 1020.5
π × 5² × 13 = 325π cm³, 325 × 3.14 = 1020.5 cm³, which is 1020.5 mL.
16. 1.5 cm
The ornament's volume equals the water lifted: the base is 50 × 30 = 1500 cm², so the rise is 2250 ÷ 1500 = 1.5 cm.
17. 48 L
The water is 30 × 40 × 40 cm³, ÷ 1000 for litres: 48 L. Or in dm first: 3 × 4 × 4 = 48 dm³ = 48 L.
18. 0.6123 m³
In cm: 3.14 × (40² − 25²) × 200 = 3.14 × 975 × 200 cm³, ÷ 1 000 000 for m³: 0.6123 m³.

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