Higher June 2018 Paper 2 Q20
20 Here is an inflated swimming ring with dimensions in centimetres.
The volume of the ring, \(V\) cm\(^3\), is given by
| \(V = 0.25\pi^2(b - a)^2(b + a)\) |
Work out the volume when \(\quad a = 20 \quad\) and \(\quad b = 30\)
Give your answer to 3 significant figures. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(0.25\pi^2(30 - 20)^2(30 + 20)\) or \(0.25\pi^2 \times 10^2 \times 50\) | M1 | oe allow use of \(\pi\) as [3.14, 3.142] |
| [12 320, 12 340.21] | A1 | may be implied |
| 12 300 or \(1.23 \times 10^4\) with no value outside [12 320, 12 340.21] seen | A1 |
Additional guidance
| \(0.25\pi^2(30 - 20)^2(30 + 20)\) 12 300 | M1 A1(implied)A1 |
| 12 300 with no incorrect working | M1A1A1 |
| 12 300.0 is not to 3 significant figures | |
| M1 gained followed by answer 12 300.0 | M1A0A0 |
| Do not allow misreads eg \(0.25\pi^2(30 + 20)^2(30 + 20)\) | M0A0A0 |
| Brackets expanded correctly and values substituted | M1 |