June 2016 Paper 2 Q17
17 A cylinder has base radius \(x\) cm and height \(y\) cm
A hemisphere has radius \(6y\) cm
The cylinder and hemisphere have equal volumes.
Work out the value of \(\ \dfrac{x}{y}\)
You must show your working. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(\pi x^2y\) | M1 | oe |
| \(\dfrac{1}{2} \times \dfrac{4}{3}\pi(6y)^3\) or \(\dfrac{2}{3}\pi(6y)^3\) or \(144\pi y^3\) | M1 | oe Only allow missing brackets if recovered in subsequent working M2 \(\dfrac{2}{3}(6y)^3 = x^2y\) oe equation eg \(\dfrac{x^2}{y^2} = 144\) M2 \(\sqrt{144}\) |
| 12 or \(\dfrac{12}{1}\) | A1 | SC2 \(\sqrt{288}\) or \(12\sqrt{2}\) or 16.97... |
Additional guidance
| 12 and \(-12\) or \(-12\) | A0 |
| Allow multiplication signs in M marks | |
| Answer only of 12 | M2 A1 |
| Answers only of 12 and \(-12\) | M2 A0 |
| Answer only of \(-12\) | M0 A0 |