Higher November 2024 Paper 6 Q10
10 A bowl in the shape of a hemisphere with radius 15 cm is used to collect raindrops.
Assume each raindrop has the volume of a sphere of radius \(3 \times 10^{-4}\) cm.
Calculate how many raindrops it takes to completely fill the bowl.
Give your answer in standard form.
You must show your working.
[The volume \(V\) of a sphere with radius \(r\) is \(V = \dfrac{4}{3}\pi r^3\).] [6]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(6.25 \times 10^{13}\) with correct working | 6 | B5 an answer equivalent to \(6.25 \times 10^{13}\) with correct working or an answer in standard form \(6.2 \times 10^{13}\) to \(6.3 \times 10^{13}\) with correct working OR M2 for \(\frac{1}{2}\ (\times)\ \frac{4}{3}\ (\times)\ \pi\ (\times)\ 15^3\) or M1 for \(\frac{4}{3}\ (\times)\ \pi\ (\times)\ 15^3\) or \(4500\pi\) or 14137 to 14139 and | Correct working requires evidence of at least M1M1 |
| M1 for \(\frac{4}{3}\ (\times)\ \pi\ (\times)\ (3 \times 10^{-4})^3\) soi A1 for \(3.6\pi \times 10^{-11}\) or \(1.13\ldots \times 10^{-10}\) oe and | eg M1 \(\frac{4}{3}\pi\)[×] their answer to \((3 \times 10^{-4})^3\) | ||
| M1dep (on M1M1) for \(\dfrac{\textit{their} \text{ volume of bowl}}{\textit{their} \text{ volume of raindrop}}\) | Their volumes must have come from use of correct formulas for hemisphere and sphere or for two spheres | ||
| Alternative method: M4 for \(15^3 \div (3^3 \times 10^{-12})\) or \(1.25 \times 10^{14}\) oe or M3 for \(\left[\frac{\frac{4}{3} \times \pi}{\frac{4}{3} \times \pi}\right] \frac{15^3}{(3 \times 10^{-4})^3}\) oe and M1dep for 0.5 × their vol. scale factor | |||
| If 0, 1 or 2 scored, instead award SC3 for answer \(6.25 \times 10^{13}\) with no or insufficient working If 0 or 1 scored, instead award SC2 for a B5 answer but with no or insufficient working If 0 scored, instead award SC1 for \(2250\pi\) or 7068 to 7070 or \(3.6\pi \times 10^{-11}\) or \(1.13\ldots \times 10^{-10}\) with no or insufficient working | |||