Higher November 2019 Paper 1 Q9
9 Here are two solids.
| volume of a hemisphere \(= \dfrac{2}{3}\pi r^3 \quad\) where \(r\) is the radius |
Which solid has the greater volume?
You must show your working. [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1: working in terms of \(\pi\) | ||
| \(\pi\ (\times)\ 4^2\ (\times)\ 10\) or \(160\pi\) or [502, 503] | M1 | oe accept 3 or better for \(\pi\) accept 480 or 496 |
| \(\dfrac{2}{3}\ (\times)\ \pi\ (\times)\ 6^3\) or \(144\pi\) or [452, 453] | M1 | oe accept 3 or better for \(\pi\) accept 0.66 or 0.67 or better for \(\dfrac{2}{3}\) accept 432 or 446(.4) |
| \(160\pi\) and \(144\pi\) or [502, 503] and [452, 453] | A1 | oe values accept 480 and 432 or 496 and 446(.4) |
| \(160\pi\) and \(144\pi\) and cylinder or [502, 503] and [452, 453] and cylinder or cylinder is \(16\pi\) greater | A1ft | ft correct decision for their \(160\pi\) and their \(144\pi\) with M1M1 scored accept 480 and 432 and cylinder or 496 and 446(.4) and cylinder |
| Alternative method 2: working without \(\pi\) | ||
| \(4^2\ (\times)\ 10\) or 160 | M1 | oe |
| \(\dfrac{2}{3}\ (\times)\ 6^3\) or 144 | M1 | oe accept 0.66 or 0.67 or better for \(\dfrac{2}{3}\) |
| 160 and 144 | A1 | oe values |
| 160 and 144 and cylinder | A1ft | ft correct decision for their 160 and their 144 with M1M1 scored |
Additional guidance
| Better than 3 for \(\pi\) could be 3.1, 3.14, 3.142 or \(\dfrac{22}{7}\) | |
| \(160\pi\) with incorrect method for hemisphere | M1M0A0A0 |
| \(144\pi\) with incorrect method for cylinder | M0M1A0A0 |
| \(160\pi\) and \(144\pi\) with incorrect decision or no decision | M1M1A1A0 |
| 160 and 144 with incorrect or no decision | M1M1A1A0 |
| Accept values given as fractions for the first A mark, but for the second A mark, they must have a common denominator. eg \(160\pi\) and \(\dfrac{432\pi}{3}\) and cylinder eg \(\dfrac{480}{3}\) and \(\dfrac{432}{3}\) and cylinder | M1M1A1A0 M1M1A1A1 |
| Working with π for one value but not the other can only score M1 eg \(160\pi\) and 144 (with or without a decision) | M1 only |
| Do not allow M1 for a correct formula as part of an incorrect formula eg \(\dfrac{1}{3} \times \pi \times 4^2 \times 10\) | M0 |