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S4 Maths: Mensuration of 3D Solids (Paper 1 (basics))
S4 Maths: Mensuration of 3D Solids (Paper 1 (basics))
Paper 1 (basics): ten questions on mensuration of 3D solids with answers and one-line notes.
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: S4 Maths: Mensuration of 3D Solids |
| Level | S4 |
02 Questions (10 items)
- FoundationA cuboid measures 3 cm by 4 cm by 5 cm. Find its volume.
- FoundationA cube has edge 6 cm. Find its volume and total surface area.
- FoundationA cylinder has radius 3 cm and height 10 cm. Find its volume in terms of pi and to three decimals.
- IntermediateA cone has radius 3 cm and height 4 cm. Find its slant height and curved surface area.
- IntermediateA sphere has radius 6 cm. Find its volume in terms of pi and to three decimals.
- IntermediateA triangular prism has a base triangle of base 6 cm and height 4 cm, and its length is 10 cm. Find the volume.
- ChallengeA cone of radius 3 cm and slant height 5 cm opens into a sector. Find the angle of the sector.
- ChallengeTwo similar cylinders have lengths in the ratio 2 : 3. Find the ratio of their volumes.
- ChallengeA cube has volume 125 cubic cm. Find its edge and total surface area.
- Error redo(Error clinic) A student writes the volume of a cone as 1/2 x pi r squared h. What is the volume of a cone with radius 6 cm and height 5 cm?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | Volume = 3 x 4 x 5 = 60 cubic cm. | The volume of a cuboid is the product of its three edges, so the unit is cubic centimetres. |
| 2 | Volume = 6 cubed = 216 cubic cm; total surface area = 6 x 6 squared = 216 square cm. | All six faces of a cube are identical, so the total surface area is the square of the edge times six. |
| 3 | Volume = pi x 3 squared x 10 = 90 pi, about 282.743 cubic cm. | Every prism or cylinder takes base area times height, and a circular base has area pi r squared. |
| 4 | Slant height = the square root of 9 plus 16 = 5 cm; curved surface = pi x 3 x 5 = 15 pi, about 47.124 square cm. | Curved surface area uses the slant height rather than the height, and the slant height comes from the right triangle formed with the radius. |
| 5 | Volume = four thirds x pi x 216 = 288 pi, about 904.779 cubic cm. | The four thirds and the cube belong together in the volume formula and must not be mixed with the four and the square of the surface area. |
| 6 | Base area = 6 x 4 / 2 = 12 square cm, so volume = 12 x 10 = 120 cubic cm. | Work out the triangular base area first and then multiply by the length; the two steps cannot be swapped. |
| 7 | Sector angle = 360 x 3 / 5 = 216 degrees. | The arc of the sector must equal the circumference of the base, so the angle shrinks in the ratio of the radius to the slant height. |
| 8 | Volume ratio = 2 cubed : 3 cubed = 8 : 27. | For similar solids the volume ratio is the cube of the length ratio, while the area ratio is only the square. |
| 9 | Edge = the cube root of 125 = 5 cm, and total surface area = 6 x 5 squared = 150 square cm. | Take the cube root of the volume to get the edge, then square the edge and multiply by six for the surface area. |
| 10 | The correct value is one third x pi x 36 x 5 = 60 pi, about 188.496 cubic cm, not one half. | A cone is one third of the prism with the same base and height, so using one half is the mistake to fix. |
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.
For any mensuration question, sketch the solid first and label the radius, the height and the slant height on the diagram. The volume of a cone or pyramid is always one third of the prism with the same base and the same height, so the factor of one third must never be dropped. The volume of a sphere is four thirds pi r cubed while its surface area is four pi r squared, so the two formulas differ only in the power and the coefficient and must be kept apart. The net of a cone is a sector whose arc equals the circumference of the base, so its angle is 360 degrees times the radius divided by the slant height. When two solids are similar, the ratio of areas is the square of the ratio of lengths and the ratio of volumes is the cube, so find the length ratio first and then square or cube it to avoid swapping the two.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.
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