Higher November 2023 Paper 3 Q14
14 A solid trophy consists of a stand and a player.
The stand is made by removing a small pyramid from a large pyramid.
Large pyramid Square base, edge 8 cm Perpendicular height 16 cm
Small pyramid Square base, edge 5 cm Perpendicular height 10 cm
| Volume of a pyramid \(= \dfrac{1}{3} \times\) area of base \(\times\) perpendicular height |
(a) Show that the volume of the stand is 258 cm\(^3\) [2 marks]
(b) The trophy is made from a metal of density 7.5 grams per cm\(^3\)
The total mass of the trophy is 2340 grams.
Work out the volume of the player. [2 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(\dfrac{1}{3} \times 8 \times 8 \times 16\) or \(\dfrac{1024}{3}\) or 341.3… or \(\dfrac{1}{3} \times 5 \times 5 \times 10\) or \(\dfrac{250}{3}\) or 83.3… | M1 | oe |
| \(\dfrac{1}{3} \times 8 \times 8 \times 16 - \dfrac{1}{3} \times 5 \times 5 \times 10 = 258\) or \(\dfrac{1024}{3} - \dfrac{250}{3} = 258\) or \(341.3… - 83.3… = 258\) | A1 | oe eg \(\dfrac{1024}{3} - 258 = \dfrac{250}{3}\) must see method or values for both pyramids must use same number of decimal places for both pyramids so their answer is exactly 258 |
Additional guidance
| \(341.3 - 83.3 = 258\) | M1A1 |
| \(341.33 - 83.3 = 258.03\) | M1A0 |
| \(341 - 83 = 258\) with no correct method seen | M0A0 |
| Answer | Mark | Comments |
|---|---|---|
| \(2340 = 7.5 \times V\) or \(\dfrac{2340}{7.5}\) or 312 or \(2340 - (7.5 \times 258)\) or \(2340 - 1935\) or 405 | M1 | oe |
| 54 | A1 |