Chapter 9 Practice Paper: Volume and Surface Area of Pyramids, Cones and Spheres — mark scheme
QuizQuipPractice Series
QQ/S2MATH/CH9
Secondary 2 · Lower Secondary Mathematics (G2 / G3)
Mark scheme
Volume and Surface Area of Pyramids, Cones and Spheres
Chapter 9 Practice Paper · Maximum mark: 30
Notes for markers
- Award one mark for each point marked [1], up to the marks shown for the part.
- Accept answers worded differently that show the same understanding.
- Units are required where the answer line shows one. ecf: allow an error carried forward.
Section A: Multiple-choice questions[10 marks]
| Question | Answer | |
|---|---|---|
| 1 | CThe one-third rule: ⅓ × base area × height. | 1 |
| 2 | A⅓ × 22/7 × 9 × 7 = ⅓ × 198 = 66 cm³. | 1 |
| 3 | D√(36 + 64) = √100 = 10. | 1 |
| 4 | B4 × 3.14 × 9 = 113.04 cm². | 1 |
| 5 | C4/3 × 3.14 × 8 ≈ 33.5 cm³. | 1 |
| 6 | A⅓ × 144 × 8 = 384 cm³. | 1 |
| 7 | D3.14 × 5 × 13 = 204.1 cm². | 1 |
| 8 | BVolumes scale with r³, and 3³ = 27. | 1 |
| 9 | CCurved 22/7 × 7 × 10 = 220, plus base 154, totals 374 cm². | 1 |
| 10 | AThe cone takes exactly one third of the matching cylinder. | 1 |
Section B: Structured questions[20 marks]
| Question | Answer and marking points | Marks |
|---|---|---|
| 1(a) | V = ⅓ × 36 × 8 = 96 cm³.
| 2 |
| 1(b) | √(8² + 3²) = √73 ≈ 8.54.
| 2 |
| 1(c) | 4 × (½ × 6 × 8.54) ≈ 102.5 cm² [1] | 1 |
| Total for Question 1 | 5 | |
| 2(a) | l = √(49 + 576) = √625 = 25.
| 2 |
| 2(b) | 22/7 × 7 × 25 = 550 cm².
| 2 |
| 2(c) | 22/7 × 49 = 154 cm² [1] | 1 |
| Total for Question 2 | 5 | |
| 3(a) | V = 4/3 × 3.14 × 27 000 = 113 040 cm³.
| 2 |
| 3(b) | 113 040 ÷ 1 000 = 113.04 L [1] | 1 |
| 3(c) | 4 × 3.14 × 900 = 11 304 cm².
| 2 |
| Total for Question 3 | 5 | |
| 4(a) | ⅓ × 22/7 × 9 × 14 = 132 cm³.
| 2 |
| 4(b) | 2/3 × 22/7 × 27 = 396/7 ≈ 56.57 cm³.
| 2 |
| 4(c) | ≈ 188.57 cm³ [1] | 1 |
| Total for Question 4 | 5 |
— End of mark scheme —