Measures and solids · Ages 13–14
Cylinders at work worksheet
Part of: Cylinders
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Cylinders at work worksheet
Measures and solids · Ages 13–14
Numsprite
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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.The cylindrical glass in the picture has a base radius of 2 cm, with water 16 cm deep. In terms of π, how many cm³ of water does it hold?
Answer:
2.The cylindrical glass in the picture has a base radius of 12 cm, with water 16 cm deep. In terms of π, how many cm³ of water does it hold?
Answer:
3.The hollow cylinder in the picture (a length of pipe) has an outer radius of 7 cm and an inner radius of 5 cm, and is 15 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 7 cm and water 6 cm deep. A stone is dropped in and sinks right under, and the water rises 2 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 11 cm and an inner radius of 9 cm, and is 19 cm long. What is the volume of the pipe itself, in terms of π?
Answer:
6.The cylindrical container in the picture has a base radius of 6 cm and water 11 cm deep. A stone is dropped in and sinks right under, and the water rises 2 cm. What is the stone's volume, in terms of π?
Answer:
7.1900 mL of water is poured into an empty cylindrical cup of base radius 4 cm. Using your calculator's π key, how deep is the water, in cm, to 3 significant figures?
Answer:
8.A cylindrical tank has a base radius of 9 cm, with water 20 cm deep. A solid cylindrical rod of base radius 6 cm and height 58 cm is stood upright on the tank's floor; it rises above the water, and none spills. How deep is the water now, in cm?
Answer:
9.A cylindrical tank has a base radius of 9 cm, with water 24 cm deep. A solid cylindrical rod of base radius 3 cm and height 51 cm is stood upright on the tank's floor; it rises above the water, and none spills. How deep is the water now, in cm?
Answer:
10.1650 mL of water is poured into an empty cylindrical cup of base radius 4 cm. Using your calculator's π key, how deep is the water, in cm, to 3 significant figures?
Answer:
Part B: Choose, or true or false (2 marks each)
11.A cylindrical container of base radius 2 cm has some water in it. 24π cm³ more is poured in, none spilling. How far does the water rise?
- A. 6 cm
- B. 24π ÷ (2π × 2) cm
- C. 24π ÷ 2π cm
- D. 24 cm
Choose the right answer
Answer:
12.A cylindrical container of base radius 4 cm has some water in it. 80π cm³ more is poured in, none spilling. How far does the water rise?
- A. 5 cm
- B. 80 cm
- C. 80π ÷ 4π cm
- D. 80π ÷ (2π × 4) cm
Choose the right answer
Answer:
Part C: Word problems (4 marks each)
13.A workshop casts a cylindrical tub of metal, with a base and no lid: outer radius 7 cm, outer height 16 cm, wall and base both 2 cm thick, and 1 cm³ of metal weighs 3 g. In terms of π: the whole tub (with the space inside) is π cm³, the space inside π cm³, the metal used π cm³, weighing π g.
Fill in each blank
Working:
Answer:
14.A florist's cylindrical bucket has a base radius of 4 cm, with water 18 cm deep. A solid cylinder of flower foam, base radius 2 cm and 53 cm high, is stood upright on the bucket's floor; it rises above the water, and none spills. In terms of π, how many cm² of the foam's side are wet?
Working:
Answer:
15.A cylindrical flask is 3 cm in base radius and 20 cm high inside. Its capacity in terms of π is π cm³; with your calculator's π key, to the nearest mL, it holds about mL of hot water.
Fill in each blank
Working:
Answer:
16.A concrete pipe is 3 m long, with an outer radius of 40 cm and an inner radius of 30 cm. Using your calculator's π key, how many m³ of concrete does it take, to 3 significant figures?
Working:
Answer:
17.A cylindrical china mug (with a base, no lid) is 8 cm across and 20 cm high on the outside, its wall and base both 2 cm thick. In terms of π, what is the mug's capacity, in cm³?
Working:
Answer:
18.A workshop casts a cylindrical tub of metal, with a base and no lid: outer radius 4 cm, outer height 12 cm, wall and base both 1 cm thick, and 1 cm³ of metal weighs 4 g. In terms of π: the whole tub (with the space inside) is π cm³, the space inside π cm³, the metal used π cm³, weighing π g.
Fill in each blank
Working:
Answer:
Show the answers and working
Cylinders at work worksheet: Answers and working
Part A: Working out and filling in
1. 64 π cm³
The water is a cylinder too: base π × 22 = 4π cm², times the depth 16: 64π cm³. How tall the glass is doesn't matter.
2. 2304 π cm³
The water is a cylinder too: base π × 122 = 144π cm², times the depth 16: 2304π cm³. How tall the glass is doesn't matter.
3. 360 π cm³
The cross-section is a ring: π × 72 − π × 52 = 24π cm²; volume 24π × 15 = 360π cm³.
4. 98 π cm³
The stone's volume equals the water it lifts: base area π × 72 = 49π, times the 2 cm rise: 98π cm³. The water's first depth isn't needed.
5. 760 π cm³
The cross-section is a ring: π × 112 − π × 92 = 40π cm²; volume 40π × 19 = 760π cm³.
6. 72 π cm³
The stone's volume equals the water it lifts: base area π × 62 = 36π, times the 2 cm rise: 72π cm³. The water's first depth isn't needed.
7. 37.8 cm
1900 mL = 1900 cm³; the base is π × 42 = 16π cm², so the depth = 1900 ÷ 16π ≈ 37.8 cm (3 significant figures).
8. 36 cm
The water keeps its volume, 81π × 20 = 1620π, but now fills only the ring round the rod: π(92 − 62) = 45π. New depth = 1620π ÷ 45π = 36 cm. The rod isn't under the water: its whole volume doesn't count.
9. 27 cm
The water keeps its volume, 81π × 24 = 1944π, but now fills only the ring round the rod: π(92 − 32) = 72π. New depth = 1944π ÷ 72π = 27 cm. The rod isn't under the water: its whole volume doesn't count.
10. 32.8 cm
1650 mL = 1650 cm³; the base is π × 42 = 16π cm², so the depth = 1650 ÷ 16π ≈ 32.8 cm (3 significant figures).
Part B: Choose, or true or false
11. A. 6 cm
The water poured in is a cylinder on the container's base: rise = 24π ÷ (π × 22) = 24 ÷ 4 = 6 cm.
12. A. 5 cm
The water poured in is a cylinder on the container's base: rise = 80π ÷ (π × 42) = 80 ÷ 16 = 5 cm.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. 784, 350, 434, 1302
Outside π × 72 × 16 = 784π; inside, radius 5 and height 14 (a base only): π × 52 × 14 = 350π; metal 784π − 350π = 434π cm³, times 3: 1302π g.
14. 96 π cm²
The new depth first: the water, π × 42 × 18 = 288π, keeps its volume but fills only the ring round the foam, π(42 − 22) = 12π, so it is 288π ÷ 12π = 24 cm deep. The wet side is a curved surface 24 cm high: 2π × 2 × 24 = 96π cm².
15. 180, 565
π × 32 × 20 = 180π cm³; with the π key, 180π ≈ 565 cm³, which is about 565 mL.
16. 0.66 m³
In cm: π × (402 − 302) × 300 = π × 700 × 300 cm³, ÷ 1 000 000 for m³, with the π key: about 0.66 m³.
17. 72 π cm³
Capacity is the inside: inner radius = 8 ÷ 2 − 2 = 2 cm (the wall is on both sides); inner height = 20 − 2 = 18 cm (a base, no lid). π × 22 × 18 = 72π cm³.
18. 192, 99, 93, 372
Outside π × 42 × 12 = 192π; inside, radius 3 and height 11 (a base only): π × 32 × 11 = 99π; metal 192π − 99π = 93π cm³, times 4: 372π g.
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