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S3 Maths: Prisms, Cylinders and Spheres – Volume and Surface Area (Paper 2: intermediate)
S3 Maths: Prisms, Cylinders and Spheres – Volume and Surface Area (Paper 2: intermediate)
The second paper runs the formulas backwards: from volume to height, from surface area to radius, plus capacity conversion.
Direct answers Write the formula first and substitute second, so the steps can be checked at a glance.
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 prism has base area 45 cm squared and length 12 cm. What is its volume?
- FoundationA cylinder has diameter 10 cm and height 7 cm. What is its volume? Take pi as 3.14.
- FoundationA cylinder has radius 4 cm and height 6 cm. What is its total surface area? Take pi as 3.14.
- IntermediateA sphere has radius 6 cm. What is its volume? Take pi as 3.14.
- IntermediateA cylinder of volume 628 cm cubed has radius 5 cm. What is its height? Take pi as 3.14.
- IntermediateA triangular prism has a triangle base of 8 cm with height 5 cm, and a length of 12 cm. What is its volume?
- ChallengeA cylinder of radius 3 cm and height 10 cm unrolls into a rectangle. What is the area of that rectangle? Take pi as 3.14.
- ChallengeA sphere has surface area 314 cm squared. What is its radius? Take pi as 3.14.
- ChallengeA cylindrical bucket of inner radius 20 cm holds water 30 cm deep. How many litres is that? Take pi as 3.14.
- Error redoFor a cylinder of diameter 10 cm and height 7 cm a student substitutes 10 as the radius and gets 2 198 cm cubed. What is the correct volume?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 540 cm³ | Base area times height gives 45 times 12, which is 540. |
| 2 | 549.5 cm³ | A diameter of 10 means a radius of 5, so 3.14 times 25 times 7 gives 549.5. |
| 3 | 251.2 cm² | The two circular ends give 100.48 and the curved part gives 150.72, so the total is 251.2. |
| 4 | 904.32 cm³ | Four thirds times 3.14 times 216 gives 904.32. |
| 5 | 8 cm | Height is volume divided by pi r squared, so 628 divided by 78.5 gives 8. |
| 6 | 240 cm³ | The triangle area is half of 8 times 5, which is 20, and 20 times 12 gives 240. |
| 7 | 188.4 cm² | The rectangle is the circumference 18.84 long and 10 high, so the area is 188.4. |
| 8 | 5 cm | Four times 3.14 times r squared equals 314, so r squared is 25 and the radius is 5. |
| 9 | 37.68 L | The volume is 3.14 times 400 times 30, which is 37 680 cm cubed, and dividing by 1 000 gives 37.68 litres. |
| 10 | 549.5 cm³ | The radius is 5, not 10, so 3.14 times 25 times 7 gives 549.5. |
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 intermediate paper uses each formula both ways: work back from the volume to a height or radius, split a cylinder surface into the curved part plus two circles, and keep 4 pi r squared for the sphere surface against 4 thirds pi r cubed for its volume.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.