Higher November 2023 Paper 2 Q14
14. The diagram below shows a square-based pyramid.
The slant height of each triangular face is 12 cm.
Diagram not drawn to scale
Calculate the volume of the pyramid.
You must show all your working. [5]
| Scheme | Marks | Comments |
|---|---|---|
| \((x^2 =)\ 12^2 - (9 \div 2)^2\) | M1 | Where \(x\) represents the perpendicular height. Accept other notation. |
| \(x^2 = 123.75\) or \((x =)\ \sqrt{123.75}\) | A1 | |
| \((x =)\ 11(.12…)\) or \(\dfrac{3\sqrt{55}}{2}\) (cm) | A1 | |
| \((\text{Volume} = )\ \frac{1}{3} \times 9 \times 9 \times 11(.12…)\) | M1 | FT their height provided M1 awarded. |
| Answers in the range 299.7 to 300.4 inclusive. | A1 | FT |
| (5) |