Easy -1.2 This is a straightforward algebraic rearrangement requiring basic manipulation (multiply by 3, divide by πh, then square root). It's simpler than average A-level questions as it involves only routine algebraic steps with no problem-solving or conceptual depth beyond GCSE-level formula rearrangement.
\(2\) for \(r^2 = \frac{3V}{\pi h}\) or \(r = \sqrt{\frac{V}{\frac{1}{3}\pi h}}\) o.e. or M1
3 marks
for correct constructive first step or for \(r = \sqrt{k}\) ft their \(r^2 = k\); M1 for subst of \(-2\) or or \(-8 + 4a + 7 = 0\) o.e. obtained eq by division by \((y + 2)\)
$[r] = [\pm]\sqrt{\frac{3V}{\pi h}}$ o.e. 'double-decker' | 3 marks |
$2$ for $r^2 = \frac{3V}{\pi h}$ or $r = \sqrt{\frac{V}{\frac{1}{3}\pi h}}$ o.e. or M1 | 3 marks | for correct constructive first step or for $r = \sqrt{k}$ ft their $r^2 = k$; M1 for subst of $-2$ or or $-8 + 4a + 7 = 0$ o.e. obtained eq by division by $(y + 2)$
The volume of a cone is given by the formula $V = \frac{1}{3}\pi r^2 h$. Make $r$ the subject of this formula. [3]
\hfill \mbox{\textit{OCR MEI C1 2006 Q1 [3]}}