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S4 Maths: Mensuration of 3D Solids (Paper 4 (error clinic))
S4 Maths: Mensuration of 3D Solids (Paper 4 (error clinic))
Paper 4 (error clinic): 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 2 cm by 3 cm by 7 cm. Find its volume.
- FoundationA cylinder has radius 2 cm and height 9 cm. Find its volume in terms of pi and to three decimals.
- FoundationA cube has total surface area 96 square cm. Find its edge and volume.
- IntermediateA cone has radius 6 cm and slant height 10 cm. Find its height and volume.
- IntermediateA sphere has radius 1.5 cm. Find its volume in terms of pi and to three decimals.
- IntermediateA triangular prism has base area 20 square cm and length 7 cm. Find its volume.
- ChallengeTwo similar solids have lengths in the ratio 4 : 7. Find the ratio of their volumes.
- ChallengeA cone has radius 2 cm and slant height 6 cm. Find the angle of the sector in its net.
- ChallengeA pyramid has a square base of side 8 cm and height 6 cm. Find its volume.
- Error redo(Error clinic) A student adds only one base when finding the total surface area of a cylinder. What is the total for radius 3 cm and height 5 cm?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | Volume = 2 x 3 x 7 = 42 cubic cm. | Multiply the three edges together; the order of multiplication makes no difference. |
| 2 | Volume = pi x 4 x 9 = 36 pi, about 113.097 cubic cm. | Base area is pi r squared, and it is then multiplied by the height. |
| 3 | Six a squared equals 96, so a is 4 cm, and volume = 4 cubed = 64 cubic cm. | Divide by six to get the area of one face, then take the square root for the edge. |
| 4 | Height = the square root of 100 minus 36 = 8 cm, and volume = one third x pi x 36 x 8 = 96 pi, about 301.593 cubic cm. | The height comes from the slant height and the radius, and the volume formula uses only the height. |
| 5 | Volume = four thirds x pi x 3.375 = 4.5 pi, about 14.137 cubic cm. | A decimal radius is cubed in the usual way, and 1.5 cubed is 3.375. |
| 6 | Volume = 20 x 7 = 140 cubic cm. | When the base area is already given, the triangle does not need to be worked out again. |
| 7 | Volume ratio = 4 cubed : 7 cubed = 64 : 343. | For similar solids the volume ratio is the cube of the length ratio. |
| 8 | Sector angle = 360 x 2 / 6 = 120 degrees. | The angle depends on the ratio of the radius to the slant height, not on the height. |
| 9 | Volume = one third x 64 x 6 = 128 cubic cm. | Take base area 64 times height 6 and divide by three, never omitting the one third. |
| 10 | Curved surface 30 pi plus two bases of 18 pi gives 48 pi, about 150.796 square cm. | A cylinder has a top and a bottom, so two circles must be added. |
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 →
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