Higher November 2019 Paper 6 Q8
8 An octahedron is formed from two identical square based pyramids.
The square bases are stuck together as shown.
The volume of the octahedron is 60 cm3.
The length of the side of each pyramid’s square base is 5 cm.
Work out the height \(h\) cm of the octahedron.
[The volume of a pyramid is \(\frac{1}{3}\) × area of base × perpendicular height] [4]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 7.2 oe nfww | 4 | M2 for \(\frac{1}{3} \times 5 \times 5 \times \frac{h}{2} = 30\) oe or \(\frac{1}{3} \times 5 \times 5 \times h = 60\) oe or \(\frac{1}{3} \times 5 \times 5 \times h = 30\) oe or M1 for \(\frac{1}{3} \times 5 \times 5\ [\times \frac{h}{2} \text{ or } \times h]\) AND A1dep for [\(h\) or \(\frac{h}{2}\) =] 3.6 or 7.2 | Condone use of \(h\) or other letter as height of pyramid M2 implied by \(\frac{30}{\frac{1}{3} \times 5 \times 5}\) or \(\frac{60}{\frac{1}{3} \times 5 \times 5}\), perhaps in stages soi 8.3[3…] or \(\frac{25}{3}\) A1 dep on their M2 Note: using V = 60 should lead to final answer 7.2, and score 4 marks. If spoilt (e.g final answer 14.4, then M2A1) |