Higher November 2021 Paper 6 Q12
12 A solid metal sphere has mass 235 g.
The density of the metal is 7.78 g/cm³.
Show that the surface area of this sphere is 46.9 cm², correct to 3 significant figures.
You must show your working.
[For a sphere with radius \(r\): Volume \(= \dfrac{4}{3}\pi r^3\) Surface area \(= 4\pi r^2\).] [6]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| Answer with at least 4 sf rounding to 46.9 with correct working | 6 | M1 for [vol =] 235 ÷ 7.78 [= 30.2…] AND M2 for \(r^3 = \dfrac{\textit{their } 30.2\ldots \times 3}{4 \times \pi}\) oe [= 7.2…] or M1 for their \(30.2 = \dfrac{4}{3}\pi r^3\) A1 for \(r = 1.93\ldots\) AND M1 for [SA =] \(4 \times \pi \times\) their \(1.93\ldots^2\) If 0 scored SC1 for [\(r =\)] 1.93… with no working | “Correct working” requires evidence of at least M1 AND M1 AND M1 ie using formulas for density, volume and surface area After their \(30.2 = \dfrac{4}{3}\pi r^3\), \(r = 1.93\ldots\) scores M2A1 Condone working in reverse for a maximum of 2 marks: M1 for \(46.9 = 4\pi r^2\) A1 for \(r = 1.93\ldots\) |