Higher June 2023 Paper 2 Q25
25 A solid sphere has a radius of 2.8 centimetres, correct to 1 decimal place.
The sphere has a mass of \(\;M\pi\;\) grams, where \(M = 260\) correct to 2 significant figures.
Work out the upper bound for the density of the sphere.
Give your answer in g/cm³ correct to 2 decimal places.
Show your working clearly.
(4)
| Scheme | Marks |
|---|---|
| 255 or 265 or 2.85 or 2.75 | B1 |
\((V =)\; \dfrac{4}{3}\pi \times (2.75)^3\) \(\left(= \dfrac{1331}{48}\pi \text{ or } 87.1137….\right)\) | M1 |
\((D =)\; \dfrac{265\pi}{\frac{4}{3} \times \pi \times 2.75^3}\) (condone missing \(\pi\) for \(265\pi\) (also may have cancelled out \(\pi\))) | M1 |
| 9.56 | A1 |
| (4) | |
| (4 marks) |
Notes
B1: for sight of a correct upper or lower bound
M1: calculation to find \(V\) using \(V = \dfrac{4}{3}\pi {r_{LB}}^3\) where \(2.75 \leqslant r_{LB} \lt 2.8\) or use of 2.85
M1: method to find UB of density, using LB of \(V\) and UB of \(M\) for correct substitution into \(D = \dfrac{\pi M_{UB}}{V_{LB}}\) where \(260 \lt M_{UB} \leqslant 265\) and \(87.11... \leqslant V_{LB} \lt 91.95...\) oe
A1: dep on M2 and all correct bounds used
allow 9.55 - 9.56