Moderate -0.5 This is a straightforward algebraic rearrangement requiring squaring both sides, expanding, collecting terms, and taking a square root. While it involves multiple steps (isolating the square root, squaring, rearranging), the techniques are standard C1 manipulation with no conceptual difficulty or problem-solving insight required—slightly easier than average due to its purely mechanical nature.
5 The volume \(V\) of a cone with base radius \(r\) and slant height \(l\) is given by the formula
$$V = \frac { 1 } { 3 } \pi r ^ { 2 } \sqrt { l ^ { 2 } - r ^ { 2 } }$$
Rearrange this formula to make \(l\) the subject.
5 The volume $V$ of a cone with base radius $r$ and slant height $l$ is given by the formula
$$V = \frac { 1 } { 3 } \pi r ^ { 2 } \sqrt { l ^ { 2 } - r ^ { 2 } }$$
Rearrange this formula to make $l$ the subject.
\hfill \mbox{\textit{OCR MEI C1 2011 Q5 [4]}}