Higher November 2017 Unit 2 Q15
15. Two similar pyramids have volumes of 3970 cm3 and 3100 cm3 respectively.
The height of the larger pyramid is 25 cm.
Calculate the height of the smaller pyramid. [3]
Height = …………………… cm
| Scheme | Marks | Comments |
|---|---|---|
| (Linear scale factor=) ∛(3100/3970) OR ∛3100/∛3970 (= 0.92…) | B1 | Or equivalent. |
| ∛(3100/3970)×25 | M1 | FT their derived linear scale factor (from ∛ ). |
| = 23(.021…cm) | A1 | Accept answer in the range of 22.9 to 23.05. Do not award this mark if an answer outside of this range is then rounded to 23. |
Alternative method (using reciprocal of volume SF)
| Scheme | Marks | Comments |
|---|---|---|
| ∛(3970/3100) (= 1.0859…) | B1 | |
| 25÷∛(3970/3100) OR 1/∛(3970/3100) × 25 | M1 | |
| = 23(.02..cm) | A1 |