Higher June 2022 Paper 6 Q20
20 Two pyramids, A and B, are mathematically similar.
Pyramid A has surface area 12 cm² and volume 8 cm³.
Pyramid B has surface area 75 cm².
Work out the volume of pyramid B.
You must show your working. [4]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 125 with correct working | 4 | M3 for [8 ×] \(\left(\sqrt{\dfrac{75}{12}}\right)^3\) or \(2.5^3\) oe or M2 for \(\sqrt{\dfrac{75}{12}}\) or \(\sqrt{6.25}\) oe implied by 2.5 or \(\frac{5}{2}\) or M1 for \(\dfrac{75}{12}\) oe implied by 6.25 | “correct working” requires evidence of at least M2 Accept ratios M3 for 8 : 125 oe or M2 for 2 : 5 oe or M1 for 4 : 25 oe |
| Alternative method: M3 for [8 ÷] \(\left(\sqrt{\dfrac{12}{75}}\right)^3\) or \(0.4^3\) oe or M2 for \(\sqrt{\dfrac{12}{75}}\) or \(\sqrt{0.16}\) oe implied by 0.4 or \(\frac{2}{5}\) or M1 for \(\dfrac{12}{75}\) oe implied by 0.16 | |||
| If 0 scored, instead award SC1 for answer 125 with no or insufficient working | |||