中文（繁體）
中文（简体）
English
S3 Maths: Prisms, Cylinders and Spheres – Volume and Surface Area (Paper 3: challenge)
S3 Maths: Prisms, Cylinders and Spheres – Volume and Surface Area (Paper 3: challenge)
The third paper works on combined solids: hollow pipes, open buckets, filling a tank and melting, all needing more than one step.
Direct answers Sketch the shape and label the radius and height before substituting, which removes about half of the slips.
01 Paper details (check answers afterwards)
| Item | Detail |
|---|---|
| Questions | 10 |
| Suggested time | 20 |
| Difficulty mix | Foundation 3 · Intermediate 3 · Challenge 3 · Error redo 1 |
| Chapter | Chapter: S3 Maths: Prisms, Cylinders and Spheres – Volume and Surface Area |
| Level | S3 Maths |
02 Questions (10 items)
- FoundationA cuboid measures 12 cm by 9 cm by 5 cm. What is its surface area?
- FoundationA cylindrical tank has inner diameter 40 cm and height 50 cm. What is its capacity in litres? Take pi as 3.14.
- FoundationA hemisphere has radius 6 cm. What is its volume? Take pi as 3.14.
- IntermediateA sphere and a cylinder both have radius 3 cm, and the cylinder is 6 cm tall. What is the difference in volume? Take pi as 3.14.
- IntermediateA hollow pipe has outer radius 5 cm, inner radius 3 cm and length 10 cm. What volume of material is there? Take pi as 3.14.
- IntermediateAn open topped cylindrical bucket has radius 7 cm and height 10 cm. What is its surface area? Take pi as 3.14.
- ChallengeA rectangular tank measures 20 cm by 15 cm inside and is filled to a depth of 8 cm. How many litres of water is that?
- ChallengeA cube of edge 6 cm is melted into 12 identical small spheres. What is the volume of each?
- ChallengeA trapezoidal prism has a base trapezium with parallel sides 4 cm and 8 cm and height 3 cm, and a length of 15 cm. What is its volume?
- Error redoFor a cylinder of radius 3 cm and height 10 cm a student uses pi d squared h and gets 1 130.4 cm cubed. What is the correct volume?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 426 cm² | The three pairs are 108, 60 and 45, and doubling their sum of 213 gives 426. |
| 2 | 62.8 L | The radius is 20, so the volume is 3.14 times 400 times 50, which is 62 800 cm cubed, or 62.8 litres. |
| 3 | 452.16 cm³ | A hemisphere is half a sphere, so two thirds times 3.14 times 216 gives 452.16. |
| 4 | 56.52 cm³ | The sphere gives 113.04 and the cylinder 169.56, so the difference is 56.52. |
| 5 | 502.4 cm³ | Pi times the difference of 25 and 9 gives 50.24, and multiplying by 10 gives 502.4. |
| 6 | 593.46 cm² | There is one circular base of 153.86 plus a curved surface of 439.6, giving 593.46. |
| 7 | 2.4 L | Twenty times 15 times 8 is 2 400 cm cubed, which is 2.4 litres. |
| 8 | 18 cm³ | Melting keeps the volume the same, so 216 divided by 12 gives 18. |
| 9 | 270 cm³ | The trapezium area is 4 plus 8 times 3 divided by 2, which is 18, and 18 times 15 gives 270. |
| 10 | 282.6 cm³ | The formula uses the radius, so 3.14 times 9 times 10 gives 282.6, while squaring the diameter makes it four times too big. |
04 What to do after marking
- After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
- Repeat the same item two days later; move to the next paper only when both attempts are correct.
- Parents only need the answer and note columns; there is no need to explain every item.
The challenge paper handles combinations and melting: subtract the inner cylinder from the outer one for a pipe, drop one circle for an open bucket, and remember melting keeps the volume fixed while capacity is always reported in litres.Tutor Registration →
Questions and answers are written originally by the TutorZone team and are not taken from any school, publisher or examination authority paper. Every value is checked by computer.